
608 F.3d 871 (2010)
UNITED STATES of America ex rel. Richard F. MILLER and Richard F. Miller, Appellees
v.
BILL HARBERT INTERNATIONAL CONSTRUCTION, INC., et al., Appellants.
Nos. 08-5390, 08-5391, 08-5392, 08-5393, 08-5394.
United States Court of Appeals, District of Columbia Circuit.
Argued December 7, 2009.
Decided June 22, 2010.
*874 Alfred W. Putman, June Ann Sauntry, Barry Coburn, Charles C. Murphy Jr., and Charles S. Leeper argued the causes for appellants. With them on the briefs were Michael R. Miner and Alicia Hickok. Bryan B. Lavine, Stephen P. Murphy, and Brian P. Watt entered appearances.
Steve Frank, Attorney, U.S. Department of Justice, and Paul R.Q. Wolfson argued the cause for appellees. With them on the brief were Douglas N. Letter, Attorney, U.S. Department of Justice, Keith V. Morgan, Assistant U.S. Attorney, Robert B. Bell, Jennifer M. O'Connor, and Annie L. Owens. R. Craig Lawrence, Assistant U.S. Attorney, and Daniel S. Volchok entered appearances.
Before: SENTELLE, Chief Judge, GINSBURG and TATEL, Circuit Judges.
Opinion for the Court filed PER CURIAM.
Separate opinion dissenting from Parts II.A.2 and II.G.4 filed by Circuit Judge TATEL.
PER CURIAM:

TABLE OF CONTENTS


  I. Background...............................................................875
 II. Analysis ................................................................877
     A. Statute of Limitations ...............................................877
        1. Relation Back Under the FCA........................................878
        2. Claims Concerning Contracts 07 and 29 .............................880
        3. Claims Against BIE ................................................883
        4. Remaining Claims...................................................885
     B. Preemption ...........................................................885
     C. Personal Jurisdiction over HUK........................................886
     D. Anderson's Settlement.................................................888
     E. BHIC Stipulation......................................................888
     F. Precluding BIE from Contesting Liability..............................890
     G. Evidentiary Issues....................................................891
        1. BIE's Guilty Plea..................................................891
        2. Expert Testimony on Cartels .......................................893



*875
        3. Ruggieri's Testimony ..............................................896
        4. Evidence of HII and HC's Wealth ...................................896
      H. Sufficiency of the Evidence .........................................898
        1. Overarching Conspiracy ............................................899
        2. HUK's Involvement in the Conspiracy ...............................901
        3. Damages ...........................................................904
III. Conclusion ..............................................................907

In this False Claims Act case, the jury found five companies and one individual liable for rigging the bidding on three contracts in Egypt funded by the USAID. Trebling the jury's award, the district court imposed over $90 million in damages. The defendants appeal, challenging several of the district court's rulings, as well as the sufficiency of the evidence adduced against them. For the reasons set forth in this opinion, we conclude (1) that the plaintiffs' claims on two of the contracts are barred by the applicable statute of limitations, and (2) that certain testimony and evidence introduced at trial unfairly prejudiced three defendants. In all other respects, we affirm.

I. Background
Following the 1978 Camp David Accords, the United States agreed to provide economic assistance to Egypt through the U.S. Agency for International Development (USAID), including funding for improving sewer systems in Cairo and Alexandria. The sewer projects were divided into numerous construction contracts and put out for bidding by contractors prequalified by the USAID.
In 1995, Richard Miller, then a Vice President of the J.A. Jones Construction Company (Jones), the 40% partner in a series of identical joint ventures that bid on three of the projects, filed a complaint under the False Claims Act (FCA). 31 U.S.C. § 3729 et seq. Enacted during the Civil War, the FCA penalizes knowingly submitting or conspiring to submit false or fraudulent claims to the United States Government, § 3729(a)(1)(A), (C), and authorizes private enforcement through qui tam actions, which give individuals knowing of fraud a monetary incentive to come forward, § 3730(b). In his complaint, Miller alleged that in the course of his employment, he discovered that the defendants, other contractors, and a variety of related corporate entities and individuals were all members of a conspiracy to rig the bidding on contracts in Egypt. This so-called Frankfurt Club would meet to discuss upcoming contract bids in Frankfurt, Germany, the home of the conspiracy's leader, Jones's parent corporation, Holzmann, A.G. Miller's complaint focused on the bidding for one particular contract, Contract 20A, and named Holzmann, Jones, Harbert International, Inc. (HII) Jones's partner on the other side of the joint ventureand several related corporations as defendants.
In accordance with the FCA, Miller filed his complaint in camera, and the district court placed it under seal. A qui tam relator suing under the FCA brings his case "in the name of the Government," § 3730(b)(1), and his initial complaint remains under seal for sixty days. Before the expiration of that period, the Government must (1) intervene and "proceed with the action, in which case the action shall be conducted by the Government," § 3730(b)(4)(A); (2) "notify the court that it declines to take over the action, in which case [the relator has] the right to conduct the action," § 3730(b)(4)(B); or (3) petition the court for an extension of the seal period by showing "good cause," § 3730(b)(3). If the Government decides to intervene, it *876 typically does so by filing an amended complaint.
In this case, soon after Miller filed his complaint, the Government opened a criminal investigation into the alleged conspiracy and, fearing that active civil litigation would interfere with that investigation, filed successive motions to keep Miller's complaint sealed. In the meantime, the Government prosecuted many of the participants in the Cairo and Alexandria bid-rigging arrangements, obtaining guilty pleas or convictions from at least five U.S. corporations or individuals.
In February 2001, the Government allowed Miller's complaint to be unsealed and filed its own Complaint in Intervention, taking over control of the case. The Government's complaint adopted the claims that Miller had asserted on Contract 20A and added claims on two other contracts, Contracts 29 and 07, which it characterized as part of the same Frankfurt Club conspiracy. It charged all the defendants with substantive FCA violations for each of the three contracts and with participating in the overarching conspiracy. Miller later amended his complaint to do the same. In essence, Miller and the United States alleged that prior to each contract, some or all of the bidders prequalified by the USAID met in Frankfurt to discuss the bidding. At these meetings or thereafter, the bidders reached an agreement that all but one would either bid high or refrain from bidding, and the winning bidder would pay these cooperators a "loser's fee."
Contract 20A, the first of the three contracts and the only one identified in Miller's original complaint, covered installation of large-diameter, underground sewer pipe in densely populated Cairo neighborhoods. The plaintiffs alleged that the joint venture between HII and Jones (Harbert-Jones), one of three prequalified bidders, sought and received commitments from the other two companies to either overbid or not bid for the contract. Thanks to this agreement, Harbert-Jones ultimately won the contract for $115 million, subsequently paying the other two bidders $2.2 and $3 million for their cooperation. The plaintiffs further alleged that in order to hide $10 million in excess profits, the joint venture engaged in a sale/leaseback transaction with an affiliated corporation.
Contract 29, the second contract, involved the construction of a wastewater treatment plant near Cairo. In this instance, Harbert-Jones allegedly met with the only other prequalified bidder and agreed to lose the bid in exchange for a $4 million loser's fee.
The third contract, Contract 07, covered the construction of sewers in Alexandria. Because this time Harbert-Jones was apparently unable to reach a bid-rigging agreement with all other qualified bidders, it entered into a bilateral agreement with one other bidder. Under that deal, the party that won the contract would compensate the other with a loser's fee. Although the record is unclear on this point, the fee would have been either 1.5 million U.S. Dollars or 1.5 million German Deutschmarks.
As relevant here, the Government's Complaint in Intervention and Miller's amended complaint named the following defendants:
 Holzmann, see supra at 4;
 Jones, see supra at 3;
 HII, see supra at 4;
 Harbert Corporation (HC), HII's parent corporation;
 Bilhar International Establishment (BIE), to which HII assigned the contracts in question after bidding was complete. (We hold, infra at 883, that the reference in the original complaint to Harbert International Establishment, *877 Inc., was intended to refer to BIE);
 Harbert Construction Services (U.K.), Ltd. (HUK), a corporation owned 49% by BIE and 51% by a private individual that provided various financial services in connection with the bidding;
 Bill Harbert International Construction, Inc. (BHIC), a corporation which, though inactive at the time of bidding, subsequently took partial ownership of BIE and allegedly provided support for fraudulent billing on inflated invoices as the ill-gotten contracts were completed.
 Bill Harbert, President of HII and a senior executive at other corporate defendants; and
 Roy Anderson, Vice President of HII and President of BIE.
Five years of pleadings, motions, and discovery followed Miller's amended complaint and the Government's Complaint in Intervention. After declaring bankruptcy and settling with the plaintiffs, Holzmann and Jones were each dismissed from the case. Trial began in March 2007, and following seven weeks of testimony, the jury found for the plaintiffs on every count. This included conspiracy by all defendants, as well as substantive violations by most defendants with respect to most of the contracts. (For some defendants' involvement in some contracts, the district court held that it lacked subject matter or personal jurisdiction. In addition, at the conclusion of testimony, the court found all claims against Bill Harbert were barred by the FCA's statute of limitations.)
The jury found that the United States suffered approximately $34 million in damages from the defendants' conduct. As required by the FCA, the district court trebled these damages and added statutory penalties. See 31 U.S.C. § 3729(a). After subtracting amounts previously recovered by the United States, it awarded $90.4 million in damages. The defendants moved for judgment notwithstanding the jury's verdict on a variety of issues and sought a new trial on others. Rejecting the defendants' legal arguments and finding the jury's verdict amply supported by the evidence, the district court denied all of the defendants' motions in a 125-page opinion. Miller v. Holzmann, 563 F.Supp.2d 54 (D.D.C.2008). This appeal followed.

II. Analysis
The defendants raise a number of issues. We first address two threshold issues whether the statute of limitations bars any claims against the defendants and whether the Foreign Assistance Act preempts the False Claims Act. We next address personal jurisdiction over HUK, the contradiction at trial of a stipulation regarding BHIC's existence, and the district court's decision to preclude BIE from contesting liability. Finally, we address the defendants' arguments concerning four evidentiary issues and the sufficiency of the evidence.

A. Statute of Limitations
As relevant here, the FCA precludes a civil action filed "more than 6 years after the date on which the violation ... is committed." 31 U.S.C. § 3731(b)(1). The violations at issue here occurred in the late 1980s and the 1990s. Miller filed his initial complaint in 1995 alleging the defendants violated the FCA in their dealings associated with Contract 20A. The Government filed its Complaint in Intervention in 2001, adopting Miller's claims concerning Contract 20A and adding its own claims concerning Contracts 07 and 29. In his Third Amended Complaint, filed in 2006, Miller too added claims concerning the latter contracts.
*878 The defendants argue the statute of limitations bars all the Government's claims and bars Miller's claims concerning Contracts 07 and 29 because the events giving rise to those claims occurred more than six years before the claims were brought. The Government and Miller argue the claims relate back to Miller's initial complaint and therefore have the benefit of the earlier filing date.[1] BIE argues separately the claims against it do not relate back because it was added as a defendant after the statute of limitations had run.
The district court held the Government's claims concerning Contracts 07, 20A, and 29, as well as Miller's claims concerning Contracts 07 and 29, relate back to Miller's initial complaint. See 563 F.Supp.2d at 139-42. We review de novo whether "claims are barred by the statute of limitations," Jung v. Mundy, Holt & Mance, PC, 372 F.3d 429, 432 (D.C.Cir.2004), and hold the statute of limitations does not bar the Government's claims concerning Contract 20A because they relate back to Miller's timely filed complaint but does bar all claims, both the Government's and Miller's, concerning Contracts 07 and 29. The district court also rejected BIE's separate argument, as do we, because BIE should have known within the required time it was an intended defendant.

1. Relation Back Under the FCA
At the time of trial the FCA did not by its terms address relation back, but the district court held the FCA nonetheless implicitly permitted an otherwise untimely claim to relate back under what is now Federal Rule of Civil Procedure 15(c)(1)(B). See 563 F.Supp.2d at 139-40 n. 137 (interpreting what was then Rule 15(c)(2)). In 2009, after trial but before this appeal was briefed, the Congress amended the FCA expressly to provide for relation back. The statute now reads:
For statute of limitations purposes, any such Government pleading shall relate back to the filing date of the complaint of the person who originally brought the action, to the extent that the claim of the Government arises out of the conduct, transactions, or occurrences set forth, or attempted to be set forth, in the prior complaint of that person.
31 U.S.C. § 3731(c).
The statute as thus amended applies to this case on appeal. Although most of the 2009 amendments to the FCA apply only "to conduct on or after the date of enactment," the provision permitting relation back was made expressly "appl[icable] to cases pending on the date of enactment." Fraud Enforcement and Recovery Act of 2009 (FERA), Pub.L. No. 111-21, § 4(f)(2), 123 Stat. 1617, 1625 (emphasis added).
The defendants' arguments that the amended statute cannot constitutionally be applied to this case are unpersuasive. The Ex Post Facto Clause of the Constitution applies only to penal legislation. See Calder v. Bull, 3 U.S. (3 Dall.) 386, 390-91, 1 L.Ed. 648, (1798) (opinion of Chase, J.); see also Landgraf v. USI Film Prods., 511 U.S. 244, 266 n. 19, 114 S.Ct. 1483, 128 L.Ed.2d 229 (1994) (citing Calder). The FCA is not penal. See Hudson v. United States, 522 U.S. 93, 100-03, 118 S.Ct. 488, *879 139 L.Ed.2d 450 (overruling Court's prior decision that a civil FCA proceeding could be criminal under the Double Jeopardy Clause). We need not address the arguments concerning the Takings and the Due Process Clauses of the Constitution because they were raised in only two conclusory sentences. See Cablevision Sys. Corp. v. FCC, 597 F.3d 1306, 1312 (D.C.Cir.2010) ("Federal courts should not... decide [a] constitutional question unless it is presented with the clarity needed for effective adjudication.") (brackets in original) (internal quotation marks omitted); Cement Kiln Recycling Coalition v. EPA, 255 F.3d 855, 869 (D.C.Cir.2001) ("A litigant does not properly raise an issue by addressing it in a cursory fashion with only bare-bones arguments.") (internal quotation marks omitted).
The defendants argue the Congress did not intend that the amendment reach cases in which the Government had already intervened because it referred to "cases pending" rather than to "all pending cases." In Lindh v. Murphy, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997), upon which the defendants rely, the Supreme Court discussed in a footnote the use and omission of "all" and "any" in statutory provisions. See id. at 328-29 n. 4, 117 S.Ct. 2059. There the Court interpreted a retroactivity provision that on its face applied only to one of several chapters in the statute. See id. at 326-27, 117 S.Ct. 2059 (quoting Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, § 107, 110 Stat. 1214, 1226 ("Chapter 154 ... shall apply to cases pending on or after the date of enactment of this Act")); see also Martin v. Hadix, 527 U.S. 343, 356, 119 S.Ct. 1998, 144 L.Ed.2d 347 (1999) (explicating Lindh). Unlike the statute interpreted in Lindh, the clause in the FERA specifying the effective date of the provision concerning relation back is not limited in scope to a particular type of case or subset of cases.
The defendants, citing the Supreme Court's recent decision in Carr v. United States, 560 U.S. ___, 130 S.Ct. 2229, ___ L.Ed.2d ___ (2010), would also have us infer, from a temporal sequence or choice of verb tense, that Congress intended to limit the effect of the statute to cases in which the Government has not yet intervened. We have no need to draw inferences, however, when the statute is clear on its face. See Robinson v. Shell Oil Co., 519 U.S. 337, 340, 117 S.Ct. 843, 136 L.Ed.2d 808 (1997) ("Our first step in interpreting a statute is to determine whether the language at issue has a plain and unambiguous meaning with regard to the particular dispute in the case. Our inquiry must cease if the statutory language is unambiguous and the statutory scheme is coherent and consistent.") (internal quotation marks deleted). The amendment "applies to cases pending on the date of enactment." Pub.L. No. 111-21, § 4(f)(2), 123 Stat. 1617, 1625. Because this case was pending on the date of enactment, the amendment applies. Q.E.D.
The defendants urge us to adopt an "equitable doctrine of relation back" and so not to allow the Government's claims to relate back in this case because it delayed filing its own complaint and unsealing Miller's complaint until several years after the statute of limitations had run. We reject this argument because the statute, as amended, permits both relation back andif good cause be shownmaintaining the relator's complaint under seal indefinitely beyond the sixty days. See 31 U.S.C. § 3730(b)(3).
Although the Government may take advantage of the relator's filing date, the FCA still does limit the claims it may add. Under the new provision, the Government's complaint can relate back to the original complaint only "to the extent that *880 the claim of the Government arises out of the conduct, transactions, or occurrences set forth, or attempted to be set forth, in the prior complaint." 31 U.S.C. § 3731(c). The defendants do not argue the scope of the Government's claims concerning Contract 20A impermissibly expands beyond that of Miller's. Accordingly we hold the Government's claims concerning Contract 20A are not barred by the statute of limitations because they relate back to Miller's original timely complaint.

2. Claims Concerning Contracts 07 and 29
In contrast, the Government's claims concerning Contracts 07 and 29 do not meet that standard because they have little to do with Miller's claims concerning Contract 20A. As we noted in Meijer, Inc. v. Biovail Corp., 533 F.3d 857 (D.C.Cir. 2008), ordinarily "[t]he underlying question [in analyzing relation back] is whether the original complaint adequately notified the defendants of the basis for liability the plaintiffs would later advance in the amended complaint." Id. at 866 (citing 6A Charles Alan Wright, Arthur R. Miller, & Mary Kay Kane, Federal Practice & Procedure § 1497 ("if the alteration of the original statement is so substantial that it cannot be said that defendant was given adequate notice of the conduct, transaction, or occurrence that forms the basis of the claim .. . then the amendment will not relate back")).
This focus upon notice is in tension with the requirement that a complaint alleging a violation of the FCA be filed under seal and not served "on the defendant until the court so orders." 31 U.S.C. § 3730(b)(2). We have not had occasion to address this tension before because in no prior case in this circuit had the Government kept the complaint under seal and refrained from serving it on the defendant until after the statute of limitations had run.[2] The Second Circuit, however, considered this tension when it held the FCA, before it was amended, did not implicitly permit relation back: "The secrecy required by § 3730(b) is incompatible with Rule 15(c)(2) [now 15(c)(1)(B)], because (as is well-settled) the touchstone for relation back pursuant to [that] Rule[] is notice." United States v. Baylor Univ. Med. Ctr., 469 F.3d 263, 270 (2006).
Under the statute as amended to allow relation back, the inquiry cannot be whether the defendant had actual notice of the claim before the statute of limitations had run because the FCA specifically requires that the complaint be filed under seal. The timely filed private party's complaint, however, still limits the permissible scope of the Government's later-filed complaint because, as mentioned above, the statute requires that in order to relate back a new claim must arise from the same conduct, transactions, or occurrences as did the timely complaint.
Cases concerning relation back under Rule 15, despite their focus upon notice to the defendant, are useful in analyzing relation back under the FCA because the standards in the FCA and in Rule 15 are substantively identical. As we have seen, the FCA allows relation back only "to the extent that the claim of the Government arises out of the conduct, transactions, or occurrences set forth, or attempted to be set forth, in the prior complaint," 31 U.S.C. *881 § 3731(c); Rule 15(c)(1)(B) allows relation back only to the extent the new pleading "asserts a claim or defense that arose out of the conduct, transaction, or occurrence set outor attempted to be set outin the original pleading."
Relation back generally is improper when the new pleading "asserts a new ground for relief supported by facts that differ in both time and type from those the original pleading set forth," Mayle v. Felix, 545 U.S. 644, 650, 125 S.Ct. 2562, 162 L.Ed.2d 582 (2005); "attempts to introduce a new legal theory based on facts different from those underlying the timely claims," United States v. Hicks, 283 F.3d 380, 388 (D.C.Cir.2002); or, although it "shares `some elements and some facts in common' with the original claim ... its effect is `to fault [the defendants] for conduct different from that identified in the original complaint,'" Jones v. Bernanke, 557 F.3d 670, 674 (2009) (quoting Meijer, 533 F.3d at 866).
Courts have refused to relate back "amendments alleging the separate publication of a libelous statement, the breach of an independent contract, the infringement of a different patent, or even a separate violation of the same statute." 6A Wright, Miller, & Kane, supra, § 1497 (footnotes deleted) (collecting cases). For example, in United States ex rel. Bledsoe v. Community Health Systems, 501 F.3d 493 (2007), the Sixth Circuit applied the relation back provisions of Rule 15 in a qui tam case involving claims for reimbursement from Medicare and Medicaid submitted under certain Current Procedural Terminology (CPT) codes used for billing medical services. The timely documents alleged improper billing under Code 94799 for services related to "emergency room" and "02 Equip./Daily" but the amended complaint also alleged "improper[] billing... under that [same] code for a `call back' charge for which no procedure is associated"; the court held the latter allegation did not relate back because the former allegation would not have "alert[ed]" the defendant that billing related to call backs was involved. Id. at 518-19. The timely documents also made "several allegations of improper billing under CPT code 99201," including allegations concerning miscoding of supplies, but the amended complaint added allegations of improper billing "for cardiopulmonary resuscitation under [that] code"; again the court held the latter allegations did not relate back because the original documents would not have "alert[ed][the][d]efendants .. . that cardiopulmonary resuscitation procedures were involved." Id. at 513, 518-19. Although in each instance the allegations in the timely documents and in the amended complaint addressed improper billing under the same billing code, the court held the new allegations did not relate back because they did not "arise from the same conduct, transaction or occurrence" involved in the timely complaint. Id. at 519.
In this case, all three contracts are similar only in that each was funded by the USAID and required work related to sewer systems in Egypt. The differences among them, however, are significant. Based upon the allegations in the complaint, the critical facts regarding each contract are the work to be performed, who was prequalified to participate in the bidding that was allegedly rigged, when the contract was awarded, who won the contract, and the amount of the winning bid. The following table summarizes these facts for each contract and thus shows the important differences.


*882
--------------------------------------------------------------------------------
                       Winning
Contract   Awarded   bid         Project       Prequalified        Recipient
--------------------------------------------------------------------------------
20A        1988      $114.9      19 km of      George A. Fuller    Harbert-Jones
                     million     underground   Co., Fru-Con        20A Joint
                                 sewer pipe    Construction Co.,   Venture
                                 in Cairo      and Harbert-Jones
                                               20A Joint Venture
--------------------------------------------------------------------------------
29         1989      $114.9      Wastewater    At least Sadelmi    Sadelmi U.S.A.
                     million     treatment     U.S.A. and
                                 plant in      Harbert-Jones 29
                                 Cairo         Joint Venture
--------------------------------------------------------------------------------
07         1990      $ 44.6      Sewer in      Morrison-Knudsen,   Harbert-Jones
                     million     Alexandria    FruCo n, Maclean    07 Joint
                                               Grove, Tidewater,   Venture
                                               and Harbert-Jones
                                               07 Joint Venture
--------------------------------------------------------------------------------

As reflected in the table, each contract required work to be performed on a different project and was awarded in a different year to a different winning bidder drawn from a different pool of prequalified bidders. Allegations concerning Contract 20A do not fairly encompass Contracts 07 or 29 because each contract is unique and no two involved the same "conduct, transaction[], or occurrence[]."
Miller and the Government argue the use of the plural in Miller's complaint "conspired to rig the bidding for construction contracts paid for by the [USAID]" (emphasis added)together with the allegation there was a "club [] organized to control prices" and the contention that "discovery in this case will reveal [] other AID contracts," broadened the scope of the complaint beyond Contract 20A. As we held in Meijer, however, using the plural form does not cause new allegations to relate back when, as here, the new allegations do not involve "conduct, transactions, or occurrences" common to the timely pleading. See 533 F.3d at 866. As in Meijer, our decision here is impelled by more than the limited relevance of the plural form. Miller's allegations concerning any contracts beyond 20A were nothing more than "`naked assertion[s]' devoid of `further factual enhancement,'" viz., the existence of a price-fixing "club," and that discovery would reveal other rigged contracts. Ashcroft v. Iqbal, ___ U.S. ___, 129 S.Ct. 1937, 1949, 173 L.Ed.2d 868 (2009) (quoting Bell Atlantic Corp. v. Twombly, 550 U.S. 544, 557, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007)) (brackets in original). Allowing such broad and vague allegations to expand the range of permissible amendments after the limitation period has run would circumvent the statutory requirement in the FCA that the amendments "arise[] out of the conduct, transactions, or occurrences" in the original complaint, 31 U.S.C. § 3731(c); it would also, we note, circumvent the recent teachings of Iqbal and Twombly by allowing amendments to relate back to allegations that were themselves nothing more than "naked assertions." That potential for abuse is avoided by the relation back provision in the FCA, the amendment of which postdates Twombly, cabining the scope of otherwise untimely amendments by imposing the same "conduct, transactions, or occurrences" requirement. 31 U.S.C. § 3731(c).
Turning to Miller's claims concerning Contracts 07 and 29, we hold they are *883 barred by the statute of limitations because he added them after the limitation period had run. Miller may not take advantage of the relation back provision in the FCA, which applies only to the Government's pleadings. See id. If his claims are to relate back then they must do so under Rule 15(c)(1)(B), which permits relation back for claims "that arose out of the conduct, transaction, or occurrence set out... in the original pleading." We need not decide whether Rule 15(c)(1)(B) applies to claims made by a relator in litigation under the FCA because we have determined the claims concerning Contracts 07 and 29 do not meet that standard, which for our purposes is substantially the same as the standard in the amended FCA.

3. Claims Against BIE
Prior to 2006 both Miller's and the Government's complaints named Harbert International Establishment, Inc. (HIE, Inc.) among the defendants; they did not name Bilhar International Establishment (BIE). In amended complaints filed in 2006, Miller and the Government replaced references to "Harbert International Establishment, Inc." with references to "Bilhar International Establishment f/k/a Harbert International Establishment." The statute of limitations bars all claims against BIE unless the amended complaints relate back to a timely complaint. The district court held the amended complaints relate back because BIE should have known it was the intended defendant. Miller v. Holzmann, 2007 WL 778599, 2007 U.S. Dist. LEXIS 15598 (D.D.C. Mar.6, 2007). We agree with the district court.

(a) History of the Companies
A company called Harbert International Establishment was formed in Liechtenstein in 1975. At all relevant times Bill Harbert owned at least part of that company and at various times BHIC and HII owned the remainder. In September 1993 Harbert International Establishment changed its name to Bilhar International Establishment. The next month a new company was formed in Liechtenstein, also called Harbert International Establishment. It acquired many of the assets of BIE (formerly HIE), including both the name Harbert International Establishment and that company's interest in Contract 20A. After transferring its assets to the new HIE, the old HIE (by then BIE) ceased operating. In 1999 Bill Harbert's son formed Harbert International Establishment, Inc. in Alabama.

(a) Analysis
Rule 15(c)(1)(C), which for present purposes is substantively the same as the version of then-Rule 15(c)(3) applied by the district court, provides an amendment relates back when:
the amendment changes the party or the naming of the party against whom a claim is asserted ... if, within the [120 days] provided by Rule 4(m) for serving the summons and complaint, the party to be brought in by amendment:
(i) received such notice of the action that it will not be prejudiced in defending on the merits; and
(ii) knew or should have known that the action would have been brought against it, but for a mistake concerning the proper party's identity.
Fed.R.Civ.P. 15(c)(1)(C) (emphasis added).
Relation back under this provision "is most obviously appropriate in cases [such as this] where the plaintiff has sued a corporation but misnamed it." Roberts v. Michaels, 219 F.3d 775, 778 (8th Cir.2000). BIE does not claim the misnaming prejudiced it and the plaintiffs do not dispute BIE's defense that it did not actually know it was the intended defendant; the dispute *884 between the parties is whether BIE should have known it was the intended defendant.
The same attorney represented BIE, HIE, and HIE, Inc. That attorney acknowledges she knew the plaintiffs had erred in naming HIE, Inc., but as between her two other clients with similar names she "felt that it was likely that the Government had intended to sue Harbert International Establishment[,] ... not Bilhar International Establishment."
In determining what BIE, in the person of its attorney, knew or should have known, we consider the allegations in Miller's Second Amended Complaint[3] as follows:


---------------------------------------------------------
Allegation                       Comment
---------------------------------------------------------
(1) BHIC "controls               BHIC owned 79%
    and operates" the            of BIE but none of
    defendant.                   HIE.
---------------------------------------------------------
(2) The defendant is "a          This allegation
    Liechtenstein corporation    does not advance
    which,                       the inquiry because
    upon information             both HIE and BIE
    and belief, has as           were organized in
    its principal place          Liechtenstein and
    of business                  neither has its
    Birmingham,                  principal place of
    Alabama."                    business in
                                 Alabama.
---------------------------------------------------------
(3) The defendant                This allegation applied,
    "holds a 49 percent          at one time
    share" of HUK.               or another, to both
                                 BIE and HIE. By
                                 the time the complaint
                                 was filed
                                 BIE had sold its
                                 49% interest in
                                 HUK to HIE.
---------------------------------------------------------
(4) Bill Harbert was             This allegation
    Chairman and Roy             applied equally to
    Anderson was                 BIE and to HIE.
    President of the
    defendant.
---------------------------------------------------------
(5) "In 1991, as a consequence   The same paragraph
    of a reorganization          describes
    of the                       HII as managing
    Harbert entities,            the 20A Joint
    Contract 20A was             Venture, suggesting
    assigned to                  the referenced
    Harbert                      assignment of
    International                Contract 20A came
    Establishment,               from HII. The
    which is owned and           paragraph better
    controlled by                describes BIE. As
    [BHIC], and these            stated above,
    companies began              BHIC owned the
    participating                majority of BIE,
    directly in the              not of HIE. The
    conspiracy."                 assignment of
                                 Contract 20A did
                                 not change in 1991.
                                 In 1989 HII assigned
                                 it to BIE,
                                 which was then
                                 known as HIE. In
                                 1993, after the new
                                 company was created
                                 and named
                                 HIE, BIE reassigned
                                 Contract
                                 20A to the new
                                 HIE.
---------------------------------------------------------

Of these five allegations, Nos. 2 and 4 are of no help in identifying the correct defendant because they favor neither HIE nor BIE. Of the three allegations that better describe one company than they do the other, only one more accurately applies to HIE: At the time of the complaint, HIE owned 49% of HUK. Allegations 1 and 5 indicate BIE was the intended defendant: BHIC, not HIE, owned the majority of BIE, and HII assigned part of its interest in Contract 20A to the company that, at the time, was named HIE and was owned primarily by BHIC. Thereafter the assignee participated in the conspiracy. This latter datum, which unlike the others reaches the intended defendant's substantive involvement in the bid rigging, should have led counsel to the conclusion that BIE was the intended defendant.
*885 This discussion undoubtedly seems obscure to anyone unfamiliar with the various companies in the Harbert group of companies. When an attorney for several of these companies, however, receives a complaint she knows mistakenly names as the defendant one company in the group, and she represents two other companies in the group with names similar to that of the named defendant, it should be obvious that she needs to consider the history and corporate structure of both companies and to determine which company is the intended defendant.
BIE argues the Government and Miller could have determined the correct name because the relevant parts of the structure of the Harbert complex were disclosed in certain financial documents of which they had copies. The appropriate inquiry under Rule 15, however, is what the intended defendant "should have known." Fed. R.Civ.P. 15(c)(1)(C)(ii). After this case had been submitted the Supreme Court clarified the issue in Krupski v. Costa Crociere S.p.A., 560 U.S. ___, 130 S.Ct. 2485, ___ L.Ed.2d ___ (2010). In Krupski the plaintiff sued Costa Cruise Lines N.V. instead of the related company Costa Crociere S.p.A.[4] Although the plaintiff could have determined the correct identity of the intended defendant, the Court explained,
Rule 15(c)(1)(C)(ii) asks what the prospective defendants knew or should have known during the Rule 4(m) period, not what the plaintiff knew or should have known. ... That a plaintiff knows of a party's existence does not preclude her from making a mistake with respect to that party's identity.
Id. at ___, slip op. at 8-9.
BIE argues for the first time in a footnote in its brief on appeal that the 120-day period in Rule 4(m), referred to in Rule 15(c)(1)(C), started to run when the suit was filed in 1995 rather than when the complaint was unsealed in 2001. We do not ordinarily consider an argument made for the first time on appeal. In any event, as we stated in Hutchins v. District of Columbia, 188 F.3d 531, 539 n. 3 (D.C.Cir. 1999) (en banc), "[w]e need not consider cursory arguments made only in a footnote."

4. Remaining Claims
To summarize, the only claims left standing are Miller's claims concerning Contract 20A, as originally pleaded and subsequently amended, and the Government's claims concerning the same contract, which relate back to Miller's claims for purposes of the statute of limitations. All the Government's and Miller's claims concerning Contracts 07 and 29 are time barred.

B. Preemption
BIE, HUK, and BHIC alone argue this case should have been dismissed because the Foreign Assistance Act (FAA), 22 U.S.C. § 2151 et seq., preempts the False Claims Act. The district court rejected this argument in Miller v. Holzmann, 2007 WL 710134 at *11, 2007 U.S. Dist. LEXIS 16105 at *35-36 (D.D.C. Mar.6, 2007). We address the question of preemption de novo, Bldg. & Constr. Trades Dep't, AFL-CIO v. Allbaugh, 295 F.3d 28, 32 (D.C.Cir.2002), and affirm.
The FAA, which governs how the United States provides aid to foreign countries, includes its own false claim provision. That provision authorizes the President to bring a suit on behalf of the United States, but does not authorize a private party to bring a qui tam action. See 22 U.S.C. *886 § 2399b(b). In contrast, the FCA allows a private party, in addition to the Attorney General, to bring a civil suit. See 31 U.S.C. § 3730(a), (b).
The defendants argue the qui tam provision of the FCA conflicts with the lack of such a provision in the FAA because "a precisely drawn, detailed statute pre-empts more general remedies." Brown v. Gen. Servs. Admin., 425 U.S. 820, 834, 96 S.Ct. 1961, 48 L.Ed.2d 402 (1976). They assert "[a]llowing a qui tam relator the right to file an action against foreign aid contractors ... would effectively nullify the FAA's more restrictive [remedial] provision." With this argument they suggest that, for fraud involving foreign aid, the false claim provision in the FAA, enacted in 1968, implicitly displaced the qui tam provision in the FCA, which has been around in some form since 1863. See Act of March 2, 1863, ch. 67, § 4, 12 Stat. at 698, Rev. Stat. § 3491.
"[W]hen two statutes are capable of co-existence, it is the duty of the courts, absent a clearly expressed congressional intention to the contrary, to regard each as effective." Morton v. Mancari, 417 U.S. 535, 551, 94 S.Ct. 2474, 41 L.Ed.2d 290 (1974). The FCA and the FAA are surely capable of co-existence. In a case involving foreign aid, such as this one, the Government could bring suit under either the FCA or the FAA. Indeed, the FCA expressly contemplates the possibility the Government will have a choice of remedy. See 31 U.S.C. § 3730(c)(5) ("the Government may elect to pursue its claim through any alternate remedy available to the Government"). A choice does not create a conflict, let alone an "irreconcilable conflict." See United States v. Batchelder, 442 U.S. 114, 118, 122, 99 S.Ct. 2198, 60 L.Ed.2d 755 (1979) ("overlapping statutes" with "partial redundancy" "fully capable of coexisting"); cf. EC Term of Years Trust v. United States, 550 U.S. 429, 435, 127 S.Ct. 1763, 167 L.Ed.2d 729 (2007) (nine-month limitations period for a claim under specific statute conflicts with four-year period provided by a more general statute).
Finally, the Government need not face the prospect posed by the defendants of a private plaintiff in a qui tam case somehow interfering in a case brought by the Government under the FAA. The FCA requires the private plaintiff to present his claim to the Government before it is served on the defendant. The Government may "proceed with the action, ... dismiss the action notwithstanding the objections of [the relator], ... settle the action... notwithstanding the objections of [the relator]," or keep the complaint under seal during an investigation. 31 U.S.C. §§ 3730(b), (c). Indeed, the FCA specifically authorizes the Government to restrict the relator's involvement, such as by limiting his discovery, if his involvement otherwise "would interfere with the Government's investigation or [with] a prosecution of a criminal or civil matter arising out of the same facts." § 3730(c)(4).
In sum, although the false claims provisions of the FAA and the FCA do overlap, the two statutes are fully capable of coexisting. Therefore, the FAA does not preempt the FCA.

C. Personal Jurisdiction over HUK
HUK challenges the district court's assertion of personal jurisdiction over it. Miller v. Holzmann, 2007 WL 778568, 2007 U.S. Dist. LEXIS 15599 (D.D.C. Mar.6, 2007); United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., 501 F.Supp.2d 51, 53 & n. 3 (D.D.C.2007). Reviewing the district court's assertion of personal jurisdiction de novo, McAninch v. Wintermute, 491 F.3d 759, 765 (8th Cir. 2007); see also FC Inv. Group LC v. IFX Markets, Ltd., 529 F.3d 1087, 1091 (D.C.Cir.2008) (reviewing dismissal), we *887 hold HUK had sufficient contacts with the United States to subject the company to the jurisdiction of its courts.
A court may exercise personal jurisdiction over a defendant not present within the forum if the defendant has "certain minimum contacts with [that forum] such that the maintenance of the suit does not offend traditional notions of fair play and substantial justice." Int'l Shoe Co. v. Washington, 326 U.S. 310, 316, 66 S.Ct. 154, 90 L.Ed. 95 (1945) (internal quotation marks deleted). The exercise of personal jurisdiction "must have a basis in some act by which the defendant purposefully avails itself of the privilege of conducting activities within the forum State, thus invoking the benefits and protections of its laws." Asahi Metal Indus. Co. v. Superior Ct. of Cal., 480 U.S. 102, 109, 107 S.Ct. 1026, 94 L.Ed.2d 92 (1987) (internal quotation marks omitted). Personal jurisdiction is proper where the defendant has "purposefully directed his activities at residents of the forum and the litigation results from alleged injuries that arise out of or relate to those activities." Burger King Corp. v. Rudzewicz, 471 U.S. 462, 472, 105 S.Ct. 2174, 85 L.Ed.2d 528 (1985) (internal quotation marks omitted).
HUK argues against personal jurisdiction based upon our decision in Creighton Ltd. v. Gov't of State of Qatar, 181 F.3d 118 (1999). There we held the Government of "Qatar lacks the minimum contacts with the United States that would make it amenable to suit here" even though it had "entered into a contract with a company based in the United States." Id. at 127-28. The contract had been "offered, accepted, and performed in Qatar." Id. at 128. In addition, the "contract was made subject to the laws of Qatar, payment was made in Qatari riyals to Creighton's bank account in Qatar, and the alleged breach occurred in Qatar." Id. HUK's contacts with the United States were a good deal more substantial than those of Qatar.
At all relevant times HUK was, not surprisingly, based in the United Kingdom. It had no office, bank account, real property, or employees in the United States. It was not a party to Contract 20A, nor was it a member of the joint venture that bid for that contract. On the other hand, HUK was intimately involved with the Harbert-Jones Joint Venture bid for Contract 20A. From 1985 to 1988, fully 50% of HUK's work was on the preparation of the bid for Contract 20A and one of its employees signed the tender. HUK knew that the United States Government was funding the contract and that all payments to HUK for work done in connection with the contract were funded by payments from the United States Government via bank accounts in the United States belonging to one of the other Harbert companies. In addition, the district court found, and HUK does not dispute, the following facts: HUK "was created by American citizens, acting as agents for ... American corporations, for the specific purpose of providing services to companies that were bidding on projects that were going to be funded by agencies of the United States." Miller v. Holzmann, 2007 WL 39371 at *7-8, 2007 U.S. Dist. LEXIS 501, *25-26 (D.D.C. Jan.8, 2007).
Considering these facts, we conclude "the defendant's conduct and connection with the forum State are such that he should reasonably anticipate being haled into court there." World-Wide Volkswagen Corp. v. Woodson, 444 U.S. 286, 297, 100 S.Ct. 559, 62 L.Ed.2d 490 (1980); see McGee v. Int'l Life Ins. Co., 355 U.S. 220, 223, 78 S.Ct. 199, 2 L.Ed.2d 223 (1957) (personal jurisdiction over Texas company proper in California court "based on a contract which had substantial connection with" that state). Accordingly, we hold *888 HUK's contacts with the United States were sufficient to give the district court personal jurisdiction over it.

D. Anderson's Settlement
For a time Anderson and the Government tried to settle the Government's case against him. He argues they reached an agreement and have an enforceable settlement; the Government argues the settlement was never made final and should not be enforced.
The district court dismissed "all of the relator's claims on all contracts against defendant Anderson, and all of the Government's claims but one claim on contract 29 against defendant Anderson ... as untimely under the FCA's statute of limitations." United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., 505 F.Supp.2d 1, 19 (D.D.C.2007). At trial Anderson was found liable for $149,615.20 on that one claim. 501 F.Supp.2d 51, 58 (D.D.C.2007).
Anderson joined the other defendants' argument that the statute of limitations bars all claims concerning Contract 29. Having agreed with the defendants on that point, we have no need to reach Anderson's alternative argument that the Government and he entered into a final and binding settlement agreement.

E. BHIC Stipulation
Prior to trial, the parties jointly stipulated that BHIC "did not exist at the time Contracts 20A, 29, [or] 07 were bid or entered into." This stipulation simplified the more complex, but mostly irrelevant, circumstances surrounding the formation of BHIC. In 1986, an entity named BLH Enterprises, Inc. was formed but had no employees or operations for six years. In December 1991, BLH changed its name to Bill Harbert International Construction, Inc. Then, in 1992, more than a year after Harbert-Jones entered into the last contract, BHIC acquired employees and began operations. At that point, BHIC also became the majority owner of BIE and provided support services such as administrative accounting to that company.
During trial, the Government introduced evidence that the defendants argue contradicted the joint stipulation of fact that BHIC did not exist at the time companies were bidding on and entering into the relevant contracts. The evidence introduced was a document submitted by BHIC in 1992 for prequalification to bid on another contract not at issue in this case. That document included the information about BLH's formation and its subsequent name change, indicating that BHIC had, in fact, existed when Harbert-Jones and other companies bid on and entered into Contracts 20A, 29, and 07. The Government emphasized this contradiction with the joint stipulation, asking Alf Hill, the project manager for Contract 20A, to read aloud the part of the document explaining BHIC's history. The Government then asked, "So according to this document which was submitted to the Government, BHIC existed since 1986, right?" The project manager replied, "Yes." Over BHIC's objection that the witness had not seen the document before and that the document had not been authenticated, the district court allowed the document to be submitted into evidence and refused to strike the testimony relating to BHIC's date of incorporation. In closing arguments, the Government pointed back to that document, saying "Why are we suing BHIC? ... Take a look at that document." The Government further clarified its point later in its closing argument, saying, "BHIC was in existence at the time Bill Harbert, Roy Anderson, and Tommy Kitchens were doing what they were doing rigging the bids, dealing with the profits on Contract[s] 20A, 07 and 29."
*889 After trial, BHIC argued in support of a new trial that this evidence was contrary to the stipulation, prejudicial, and undermined the credibility of BHIC counsel, who relied in opening statements on the joint stipulation. The district court denied BHIC's motion for a new trial, and clarified its reasoning for allowing the Government to introduce the evidence that BHIC had incorporated in 1986:
[P]laintiffs did not stipulate that neither BHIC nor any predecessor company existed `at the time Contracts 20A, 29, 07 were bid or entered into.' Plaintiffs did not seek to disprove the stipulated fact that BHIC did not exist prior to 1992. Rather, they sought to prove that BHIC, by its own admission, is a direct outgrowth of any entity that did exist when the bid-rigging occurred.
Miller v. Holzmann, 563 F.Supp.2d 54, 104 n. 61 (D.D.C.2008).
Even if the stipulation is read so narrowly, the Government violated it. The Government elicited testimony and claimed in closing argument that BHIC itself existed since 1986, not that a BHIC predecessor existed since then. Not only that, but the evidence establishes BLH was not in fact a predecessor to BHIC, but actually the same company. The only difference was a change in name. The document introduced by the Government included the articles of incorporation for BLH and the amendment to those articles that change its name to BHIC. The evidence did not seek to prove BHIC was an "outgrowth" of another entity. It established that BHIC existed at the time of the contract bidding.
Stipulations of fact bind the court and parties. Gander v. Livoti, 250 F.3d 606, 609 (8th Cir.2001); see also Verkouteren v. District of Columbia, 346 F.2d 842, 844 n. 2 (D.C.Cir.1965). This is their very purpose, their "vital feature." 9 Wigmore, Evidence § 2590 (Chadbourn rev. 1981). Once a stipulation of fact is made, "the one party need offer no evidence to prove it and the other is not allowed to disprove it." Id. § 2588. When the Government claimed that BHIC existed since 1986, it directly contradicted the joint stipulation that BHIC did not exist until after the bidding for the three contracts.
The contradictory statements constitute substantial prejudice to BHIC. In his opening argument, BHIC's counsel emphasized the stipulated fact, saying, "[I]f you remember those key events, the last of those was in May 1991, more than a year before BHIC begins its operations in July of 1992. The plaintiffs do not and will not contest that BHIC did not even come into existence, it didn't even exist at the time that Contracts 20A, 29 and 07 were bid and entered into." We agree with BHIC that allowing the Government to contradict the stipulation called into question the credibility of BHIC's counsel, severely impeding counsel's ability to effectively advocate for his client. The district court recognized this problem, but stated that it had "confidence that after hearing testimony concerning the complex corporate restructuring from which most of these defendants emerged, the jury was able to appreciate the distinction between plaintiffs' argument [that BLH ultimately became BHIC] and the stipulated fact." 563 F.Supp.2d at 104 n. 61. But we do not immediately see what distinction separates the Government's assertion that "BHIC existed since 1986," and the stipulated fact that "BHIC did not exist at the time Contracts 20A, 29, 07 were bid or entered into." We therefore cannot conclude that the jury made such a distinction. The district court abused its discretion when it allowed the Government to contradict the stipulation and thereby undermine BHIC's defense. We remand for a new trial for BHIC.


*890 F. Precluding BIE from Contesting Liability
The district court held that BIE was estopped from contesting liability under the FCA as to Contracts 20A and 29 because of its guilty plea in a separate criminal proceeding. United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., 2007 WL 851857, 2007 U.S. Dist. LEXIS 17667 (D.D.C. Mar.14, 2007). In February 2002, BIE pleaded guilty to an indictment charging violations of the Sherman Act, 15 U.S.C. § 1, by its involvement in the bid-rigging conspiracy from 1988 to 1996. BIE contends that it was error to preclude it, based on the doctrine of collateral estoppel, from contesting liability under the FCA because a Sherman Act conspiracy does not require an overt act, while an FCA conspiracy does. Therefore, BIE argues, it might have been able to show that although it was guilty of a Sherman Act violation, it was not liable under the FCA. As BIE sees it, because collateral estoppel affects only issues that were actually litigated and necessarily decided in the first action, Jack Faucett Assocs. v. Am. Tel. & Tel. Co., 744 F.2d 118, 125 (D.C.Cir.1984), issues relating to the overt acts necessary for the FCA conspiracy were not precluded by the guilty plea in the Sherman Act prosecution, which did not require the proof of such acts. The district court disagreed, reasoning that the overt acts BIE admitted in its guilty plea and accompanying memorandum were essential to its Sherman Act plea because they supplied the factual basis for the plea. Miller v. Holzmann, 563 F.Supp.2d 54, 80-81 (D.D.C.2008). The district court reasoned that the preclusive effects of a guilty plea in a prior criminal proceeding extend not only to the essential elements of the crime charged, but also to the facts admitted in the accompanying Rule 11 proceeding. As the court explained, Rule 11 "mandates that before entering judgment on a guilty plea, a court must `mak[e] such inquiry as shall satisfy it that there is a factual basis for the plea.'" Id. at 79 (quoting Fed. R.Crim.P. 11(f) (brackets in the district court opinion)). Thus, because the facts admitted in the Rule 11 proceeding are essential to the entry of judgment, it is consistent with the underpinnings of the collateral estoppel doctrine that a defendant should be precluded from relitigating those facts as well as those related to the essential elements of the crime. Therefore, the court concluded that having admitted liability with respect to Contracts 20A and 29 in the previous proceeding, BIE was properly precluded from contesting its liability for conspiracy with respect to those contracts. Id. at 81.
We need not ultimately decide this issue. The district court relied not only on collateral estoppel, but also on the equitable doctrine of judicial estoppel, which states that if a party successfully assumes a certain legal position in one proceeding, "he may not thereafter, simply because his interests have changed, assume a contrary position." Id. at 81 n. 14 (quoting Davis v. Wakelee, 156 U.S. 680, 689, 15 S.Ct. 555, 39 L.Ed. 578 (1895)). As applied to BIE's circumstances, the court found that BIE was advancing a position contrary to the one the criminal court relied on when it accepted BIE's guilty plea, and that judicial estoppel was therefore appropriate. Id.
Before this court, BIE has not asserted any error in this alternative reason for estopping BIE. Because BIE has forfeited the argument that the judicial estoppel was erroneous, we need go no further in our analysis. Even if we were to reject the district court's reasoning on the collateral estoppel theory, we would nonetheless affirm its ruling precluding BIE from contesting liability. See Kauthar SDN BHD v. Sternberg, 149 F.3d 659 (7th Cir.1998) ("in situations in which there is one or *891 more alternative holdings on an issue, ... failure to address one of the holdings results in a waiver of any claim of error with respect to the court's decision on that issue").

G. Evidentiary Issues
The defendants argue the district court committed reversible error in four evidentiary rulings: (1) admitting into evidence against all defendants BIE's prior guilty plea; (2) allowing the Government to present expert testimony on the economics of generic cartels; (3) allowing Luigi Ruggieri, an officer of the company that received Contract 29, to testify about his subordinate's meeting with Peter Schmidt, a Holzmann executive in Frankfurt; and (4) permitting the Government to question a witness about the wealth of HII, HC, and a related management company that was not a defendant in this case. We review for abuse of discretion the district court's decisions to admit evidence. United States v. Watson, 409 F.3d 458, 462 (D.C.Cir.2005). However, to the extent the defendants argue the district court misinterpreted the Federal Rules of Evidence, we review those interpretations de novo. United States v. Gewin, 471 F.3d 197, 200 (D.C.Cir.2006). Applying those standards, we hold that the district court did not err in the first two decisions. We also hold that Ruggieri's testimony was irrelevant to the remaining Contract 20A claims, and therefore that claim is moot. We do, however, hold that allowing the Government to elicit evidence of HII and HC's wealth constituted an abuse of discretion. Therefore, claims against HII and HC must be remanded for new trial.

1. BIE's Guilty Plea
As explained above, see supra at 33, BIE pleaded guilty to violating the Sherman Act, 15 U.S.C. § 1, by engaging in the bid-rigging conspiracy. Pursuant to Rule 11 of the Federal Rules of Criminal Procedure, BIE also submitted a memorandum describing the conspiracy and BIE's role. This guilty plea and accompanying memorandum explained that BIE and others rigged bids by "submitting bids on USAID-funded Contracts 20A, 29 and 07" and "making payments to co-conspirators who agreed to not compete for USAID-funded contracts 20A and 08 pursuant to the bid-rigging conspiracy." Pl.Ex. 562A, at Joint App'x Pl. Exs. 568-69 (Joint Rule 11 Memorandum, United States v. Bill Harbert Int'l, No. 01-00302, 2002 WL 34377422 (N.D.Ala. Feb. 4, 2002), as redacted).
When the Government sought to introduce evidence of BIE's guilty plea in the district court, the defendants argued that admitting the guilty plea and accompanying Rule 11 memorandum into evidence would improperly impute BIE's involvement to the remaining defendants. The district court disagreed, concluding that the plea and accompanying memorandum were evidence of the factual admissions therein, and were therefore "relevant pieces of evidence that are admissible against all defendants." United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., Civ. No. 95-1231, slip op. at 4 (D.D.C. Mar. 21, 2007) (Mem. Op. & Order Den. Mot. to Sever). Of course, the plaintiffs would "still bear the burden of establishing a link between the `others' who BIE allegedly conspired with, and specific defendants in this case." Id. at 4 n. 3. The court therefore allowed the Government to use the plea in its opening statement and again at the end of its case-in-chief, when counsel read the text of the memorandum to the jury.
The defendants contend that this use of BIE's guilty plea should have been excluded as hearsay. They dispute the plaintiffs' contention that it is admissible under the hearsay exception set forth in Federal *892 Rule of Evidence 803(22). They further argue that the danger of unfair prejudice substantially outweighed its probative value. See Fed.R.Evid. 403. We disagree.
Rule 803(22) permits a judge to admit "[e]vidence of a final judgment, entered after a trial or upon a plea of guilty ... to prove any fact essential to sustain the judgment, but not including, when offered by the Government in a criminal prosecution for purposes other than impeachment, judgments against persons other than the accused." First, we note that the exception to Rule 803(22)the clause beginning "but not including"does not apply. Because this case is not a criminal prosecution, the rule does not preclude introduction of the plea documents as evidence of the judgment "against persons other than the accused" (i.e., the other defendants) for reasons other than impeachment. That is, because this is a civil case, BIE's guilty plea may be admitted under Rule 803(22) against all the defendants as long as the plea was admitted "to prove any fact essential to sustain the judgment."
The defendants argue the guilty plea was not admitted to establish any fact. Instead, they assert, BIE's guilty plea was submitted only as evidence of the legal conclusion that BIE was guilty of conspiracy. But the Rule 11 memorandum clearly states more than the bare conclusion that BIE was guilty. Instead, it asserts the several facts already mentioned: that BIE and others submitted bids and made payments as part of a bid-rigging conspiracy involving Contracts 20A, 29, and 07. Each of those facts is essential to sustain the legal conclusion of BIE's guilt under Section 1 of the Sherman Act, and therefore fell within the scope of the rule. Other facts that were not essential to that conclusionsuch as specific references to the defendantswere redacted by the district court. See United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., 2007 WL 842079, 2007 U.S. Dist. LEXIS 18560, at 3 (D.D.C. Mar.16, 2007). We hold therefore that the district court properly interpreted the scope of Rule 803(22) and properly admitted BIE's guilty plea and Rule 11 memorandum under that rule.
Nor was the admission of BIE's guilty plea improper under Rule 403. Rule 403 states that relevant evidence may be excluded if, inter alia, the evidence's "probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury." Fed.R.Evid. 403. But to quote the district court, "properly admitted but potentially incriminating evidence does not equate to unfairly prejudicial evidence that must be excluded." United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., Civ. No. 95-1231, slip op. at 4-5, 2007 WL 6370493 (D.D.C. March 21, 2007) (Mem. Op. & Order Den. Mot. to Sever). In assessing prejudice and probativeness, the district court, not this court, "is in the best position to perform this subjective balancing." United States v. Cassell, 292 F.3d 788, 795-96 (D.C.Cir.2002) (quoting United States v. Washington, 969 F.2d 1073, 1081 (D.C.Cir.1992)). We are therefore "extremely wary of second-guessing" the district court, United States v. Law, 528 F.3d 888, 898 (D.C.Cir.2008) (quoting Henderson v. George Wash. Univ., 449 F.3d 127, 133 (D.C.Cir.2006)), and review its decision "only for `grave abuse,'" Cassell, 292 F.3d at 796 (quoting Washington, 969 F.2d at 1081).
BIE's guilty plea did carry with it the potential to cause prejudice or confuse the juryit might have presumed that the "co-conspirators" referred to in the plea were the other defendants in the case. The district court recognized that potential, acknowledging that the "documents pose certain problems insofar as they refer to other parties who are defendants here," *893 United States ex rel. Miller v. Bill Harbert Int'l Constr., Inc., 2007 WL 842079, 2007 U.S. Dist. LEXIS 18560, at 3 (D.D.C. March 16, 2007), and that a jury might assume the other parties were also guilty under BIE's plea just because the case caption listed them. Therefore, the court struck any names other than BIE's in the case caption and elsewhere on the document. See id. With that redaction, the court held that "the recitation of facts admitted to by BIE is highly probative, and, under these conditions [of redaction], poses relatively little risk of undue prejudice." Id. at 3-4. The court further mitigated the potential problem by twice instructing the jury that "[t]he fact that BIE pleaded guilty may not in any respect be considered against any other defendants, nor may any inference be drawn against them by reason of BIE's plea of guilty." Given these protective measures against undue prejudice, the district court clearly did not abuse its discretion in admitting against all defendants the evidence of BIE's guilty plea.
HII separately argues the guilty plea was particularly prejudicial to it because the Government implied in its opening statement that HII was trying to avoid responsibility. According to HII, this implication would look particularly reprehensible when juxtaposed with BIE's guilty plea. The jury, HII asserts, might have seen the guilty plea as evidence of BIE "taking responsibility" while HII avoided doing the same. Again, we disagree. HII's argument rests on a short passage from the Government's opening statement, in which counsel argued that "just because [HII] assigned [the contracts] out to Harbert International Establishment, they don't assign away their responsibilities." As the plaintiffs argue, that brief comment did not suggest that HII had been implicated in the earlier criminal case against BIE, but instead noted only "that HII did not escape liability for its own actions when it assigned Contracts 20A and 07 to BIE." Thus, the Government's comment does not disturb our holding that the district court did not abuse its discretion in admitting against all defendants the evidence of BIE's guilty plea.

2. Expert Testimony on Cartels
Preston McAfee, a professor of economics and business strategy at California Institute of Technology, testified for the Government as an expert witness on how bid-rigging cartels work. McAfee had no direct knowledge of the facts in this case, and testified that he had not examined the evidence to conclude whether there actually was any bid rigging in this case. Instead, he testified about "how auction and bidding work, how collusion in auctions work[s], and the incentives that are created for seeking cost-reducing technologies." For example, he explained that an economically rational member of a cartel must factor into its calculation of costs the risks associated with bid rigging (i.e., being found out and prosecuted). The cartel member's bid must be higher than that of a competitive bidder in order to cover those costs. McAfee also explained what could be inferred from the assumption that a cartel existed. For example, he testified that if a cartel existed, one could infer that members of the cartel must be able to successfully influence the bidding process if they are to succeed in the object of the conspiracythat is, rigging the bids. But the individual who prepares the bid need not know about the cartel, as long as that person is "influenced by somebody who knows about the cartel." In sum, the professor explained that "[c]artels are formed... to subvert competition and increase prices" and testified how a cartel member achieves that purpose.
Rule 702 of the Federal Rules of Evidence provides that "[i]f scientific, technical, *894 or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise." Fed.R.Evid. 702. However, not all scientific testimony is created equal; some expert opinions are more helpful or more valid than others. Recognizing this fact, in 1993, the Supreme Court in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), held that trial judges must act as gatekeepers to exclude unreliable expert testimony. Under Daubert and the Court's further clarification in Kumho Tire Co. v. Carmichael, 526 U.S. 137, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999), testimony admitted under Rule 702 must be both reliable and relevant. Id. at 152, 119 S.Ct. 1167. In 2000, the Supreme Court amended Rule 702 to reflect the Daubert line of cases, outlining general standards that the trial court must use to assess the reliability and relevance of testimony. An expert witness may therefore testify only "if (1) the testimony is based upon sufficient facts or data, (2) the testimony is the product of reliable principles and methods, and (3) the witness has applied the principles and methods reliably to the facts of the case." Fed.R.Evid. 702.
The defendants moved in limine to exclude McAfee's testimony, arguing the testimony did not meet the standards of Rule 702 because it was too broad, too generic, and based too heavily on assumptions rather than analysis of the actual evidence. They argued that McAfee's testimony was not related to the facts of the case. Instead, McAfee simply assumed that a cartel actually existed between the defendants and other companies in order to make his testimony relevant. The defendants also stressed that McAfee had not tried to determine whether a cartel existed in this case, even though there are economics-based strategies to identify whether bids are in fact collusive. Because of these weaknesses, McAfee's testimony would not assist the jury in understanding the evidence as required by Rule 702.
The district court denied the motions, and reaffirmed and explained its decision when it denied motions for a new trial. In its opinion denying a new trial, the court explicitly held that McAfee's testimony satisfied the requirements of Daubert and Rule 702. Miller v. Holzmann, 563 F.Supp.2d 54, 96 (D.D.C.2008). Quoting the advisory committee's note to Rule 702, the court stated that in some cases an expert may give valuable testimony to the factfinder by explaining general principles "without ever attempting to apply these principles to the specific facts of the case." Id. at 90 (quoting Fed.R.Evid. 702 advisory committee's note) (emphasis omitted). According to the advisory committee's note, "[f]or this kind of generalized testimony, Rule 702 simply requires that: (1) the expert be qualified; (2) the testimony address a subject matter on which the factfinder can be assisted by an expert; (3) the testimony be reliable; and (4) the testimony `fit' the facts of the case." Fed. R.Evid. 702 advisory committee's note. The district court initially held that McAfee was a qualified expert. 563 F.Supp.2d at 92 & n. 40; see also id. at 96 (listing McAfee's credentials as evidence that he was "well-qualified to testify on generally-accepted economics principles"). The court then proceeded to analyze McAfee's testimony under the rest of the advisory committee's note's rubric, first assessing relevance (addressed by the second and fourth criteria), then reliability (addressed by the third).
First, the district court held McAfee's testimony to be relevant. The testimony addressed a subject matter appropriate for *895 expert testimonythe second criterion under the Rule 702 advisory committee's notebecause McAfee explained complex processes and economic theory such as the federal government's procurement process, auction incentives, and the effect of collusion on auctions. Id. at 92. These topics "are precisely the sort of specialized, technical matter concerning which a lay jury may benefit from a qualified expert's tutelage." Id. The testimony also "`fit' the facts of the case" as required by the fourth criterion. The defendants argued that the assumptions on which McAfee based his testimony were not based in the facts of the case, and therefore did not "fit." But the district court disagreed. The court pointed out that, contrary to the defendants' assertions, "McAfee never assumed that a cartel existed in this case." Id. at 94. Instead, McAfee made it clear he was describing generic circumstances, "leaving the jury to determine which scenario best `fit' the facts in this case." Id.; see also id. at 94 n. 45 (holding that McAfee's testimony also did not create unfair prejudice under Rule 403 because he "repeatedly" explained he was not familiar with the facts, and that he did not know whether collusion occurred here). His testimony, while not derived from the facts in the case, was sufficiently connected to the facts to be relevant and helpful to the jury. Id. at 95.
Last, the district court turned to the third criterionreliabilitynoting that "the law grants a district court the same broad latitude when it decides how to determine reliability as it enjoys in respect to its ultimate reliability determination." Id. at 95 (quoting Kumho, 526 U.S. at 141-42, 119 S.Ct. 1167). Citing Daubert's observations about how to determine whether expert testimony is reliablefrom whether a theory has been subjected to peer review, to its potential rate of error, to whether a theory is generally accepted in the relevant fieldthe court determined that McAfee's testimony was reliable. Id. at 96. McAfee has published over twenty peer-reviewed articles on his theories about the nature of auctions and bidding. His testimony on economics "embodied basic principles" that are "taught in undergraduate economics courses" and "generally accepted in the field of economics." Id. Therefore, concluded the district court, McAfee's testimony satisfied the reliability criterion.
As the preceding summary of the court's reasoning demonstrates, the district court thoroughly and thoughtfully analyzed the application of Rule 702 to McAfee's testimony. We also note that district courts have "broad discretion in determining whether to admit or exclude expert testimony." United States v. Gatling, 96 F.3d 1511, 1523 (D.C.Cir.1996). The court clearly did not abuse that discretion.
The defendants also argue that McAfee's testimony should have been excluded under Rule 403 because the professor used "highly charged terms" such as "cartel member" and "colluders," and even once made an analogy to bank robbers. As Daubert explained, Rule 403 exclusion based on unfair prejudice is particularly important in the case of expert evidence, which "can be both powerful and quite misleading because of the difficulty in evaluating it." 509 U.S. at 595, 113 S.Ct. 2786 (quoting Jack B. Weinstein, Rule 702 of the Federal Rules of Evidence Is Sound; It Should Not Be Amended, 138 F.R.D. 631, 632 (1991)). But, as explained above, see supra at 38, the district court is best able to apply the balancing test of Rule 403 and determine whether evidence's potential for undue prejudice substantially outweighs its probative value. This is true for expert testimony as well as for other types of evidence. Mindful, therefore, of our responsibility not to second-guess the district court's application of the Rule 403 *896 balancing test, we conclude the district court did not improperly apply the rule here. McAfee used terms descriptive of the theories he explained, but he also repeatedly emphasized that he was not applying the terms to the facts in this case or these defendants. The district court did not abuse its discretion when it determined that McAfee's use of terms like "cartel members" and "colluders" did not make his testimony's potential for undue prejudice substantially outweigh its probative value. Indeed, it is difficult to conceive of expert testimony relevant to the issues of this case in which the witness would not employ terms like "cartel members" and "colluders." We note that Rule 403 provides the exclusion of evidence if its "probative value is substantially outweighed by the danger of unfair prejudice," not simply "prejudice." In some sense, any evidence that is probative might be arguably prejudicial. That is, the purpose of offering evidence is to influence the decision of the jury. We can hardly say that the district court abused its discretion by admitting expert testimony that used terms entirely relevant to the issues at trial.

3. Ruggieri's Testimony
Luigi Ruggieri was an officer of Asea Brown Boveri Ltd., the parent company of Sadelmi U.S.A., Inc. (SUSA), the company that received Contract 29. Over the objection of the defendants, the district court allowed Ruggieri to testify about a conversation he had with his subordinate, Giovanni Greselin, about a meeting between Greselin and Peter Schmidt, the Holzmann executive who hosted the conspiracy meetings in Frankfurt. In his testimony, Ruggieri stated that Schmidt met with Greselin and a "gentleman from Harbert" in Frankfurt. There, Schmidt proposed to Greselin that they agree on which of their companies would bid lower for Contract 29, with compensation going to the losing bidder. Ruggieri also testified, without objection from the defendants, to his personal involvement in the conspiracy. He said that he saw, then shredded, a document signed by Greselin outlining the bid rigging between Harbert-Jones and SUSA. Ruggieri then authorized Greselin to go ahead with the agreement and pay Harbert-Jones a loser's fee in cash.
Ruggieri's testimony dealt only with the bid rigging of Contract 29. We have already dismissed all the claims against the defendants regarding Contract 29 for violation of the statute of limitations. See supra at 24-25. The defendants do not argue that the part of Ruggieri's testimony to which they objecthis testimony about the conversation between Greselin and Schmidttainted the jury's consideration of the remaining claims under Contract 20A or provided the only link between any one of the defendants and the conspiracy involving 20A. Therefore the defendants' arguments regarding the admissibility of Ruggieri's testimony under Fed.R.Evid. 801(d)(2)(E) are moot. We need not address them here.

4. Evidence of HII and HC's Wealth
Raymond Harbert is Bill Harbert's nephew and CEO of Harbert Management Company, a company formed in 1993 (after most of the underlying events in this case) that manages assets for third parties, including HC. When Raymond Harbert testified, Miller's counsel asked him about the assets of HII, HC, and Harbert Management Company. From the exchange, counsel elicited that HII currently owns or is associated with seven or eight power plants in California, owns various cash assets, and makes approximately $40 to $50 million in annual revenues. Raymond Harbert also confirmed that between approximately 1990 and 1993, HII sold somewhere between $250 million *897 and $500 million in assets, including selling its 50% ownership in BIE. Raymond Harbert also testified that HC was a holding company with assets in the form of stock in subsidiary companies, and that Harbert Management Company currently manages over $100 million in assets for HC. He also testified that Harbert Management Company manages assets for other Harbert entities, including individuals of the Harbert family, for a total of around $9 billion in assets. In its closing, the Government recalled this testimony and juxtaposed the wealth of all the Harbert companies with the relative poverty of those in countries benefitting from projects funded by the USAID, saying that the excess money the Government paid to the conspirators "could have [been] used for less fortunate people in other countries."
Counsel for HII and HC objected to this testimony on the grounds that information about the companies' wealth was both irrelevant and prejudicial, and reiterate this argument on appeal. We agree. To be admitted, evidence must be relevant. Fed.R.Evid. 402. That is, the evidence must have a "tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Fed.R.Evid. 401. None of Raymond Harbert's testimony described above satisfies this definition. No fact concerning the present size and scope of Harbert Management Company was of consequence to the determination of the action. The present size and scope of Harbert Management Company, a company that was not a defendant and manages assets for many non-defendants, including Raymond Harbert, his mother, and other members of the Harbert family, had nothing to do with the liability of any of the defendants or the measure of damages. Indeed, the district court recognized this irrelevance in its opinion denying a new trial, though it deemed the irrelevant evidence not prejudicial. 563 F.Supp.2d at 111 n. 73. However, arguments to the jury about a defendant's wealth are grounds for new trial. Koufakis v. Carvel, 425 F.2d 892, 902 (2d Cir.1970) ("Remarks ... which can be taken as suggesting that the defendant should respond in damages because he is rich and the plaintiff is poor, are grounds for a new trial.") (citing Washington Annapolis Hotel Co. v. Riddle, 171 F.2d 732, 740 (D.C.Cir.1948) ("A mistrial should have been declared on account of these remarks [suggesting that the defendant should respond in damages because it was rich and the plaintiff poor].")).
Nor was evidence of the wealth of HII and of HC relevant. The district court said the testimony concerning HII and HC was properly admitted because it could help the jury decide whether one company was the alter ego of the other, a theory presented by the Government as a way to implicate HC in the conspiracy. 563 F.Supp.2d at 111. "Under the alter ego theory, the court may ignore the existence of the corporate form whenever an individual so dominates an organization `as in reality to negate its separate personality.'" Founding Church of Scientology of Wash., D. C., Inc. v. Webster, 802 F.2d 1448, 1452 (D.C.Cir.1986) (quoting Quinn v. Butz, 510 F.2d 743, 758 (D.C.Cir.1975)). Applied to this case, HII would be the alter ego of HC: if the jury had decided HII was part of the conspiracy, and that it was the alter ego of HC, the jury could have found HC liable for the conspiracy even if there was no direct evidence that HC had itself joined the conspiracy. But the evidence described above does not help establish whether HII was the alter ego of HC. Instead, Raymond Harbert testified only as to how much money HII made from selling assets in the 1990s, how much money HII makes now, and how many assets HC now has. Under Rule 401's terms, the *898 evidence made it no "more probable or less probable" that one corporation was the alter ego of the other. The only way the information could have affected the jury was to prejudice it.
The Government and Miller argue before us that all the testimony at issue was nonetheless admissible because the counsel for HII and HC brought up the subject of its wealth first, and in any case "the amount of wealth evidence elicited and referred to at trial was not large and was not significant enough" to warrant a new trial. We disagree on both points. First, the plaintiffs cite only two references to support their "But they started it!" argument: counsel's opening and closing statements.[5] Neither reference is convincing. The first time HII and HC's counsel referenced the corporations' money was to point out Miller's monetary interest in the case. This is a perfectly acceptable point for counsel to make. Cf. United States v. Smith, 232 F.3d 236, 242 (D.C.Cir.2000) ("Routinely, defense counsel cross-examines government witness about an informant's bias whether it be a plea agreement, a financial arrangement, or both."); 3 Federal Jury Practice and Instructions § 101.43 (5th ed.) (jury instruction stating that, in assessing the credibility of a witness, jury may consider whether the witness has any bias or prejudice). It is unrelated to the testimony later elicited by the plaintiffs about the various Harbert companies' wealth. Even less convincing is the plaintiffs' reliance on counsel's closing statements, which of course came after the plaintiffs had already elicited Raymond Harbert's testimony.
As for the argument that there was not enough prejudice to warrant a new trial, again we disagree. Evidence need not be reinforced and reiterated again and again for it to be prejudicial enough to warrant a new trial. Here, it is enough that there were several inappropriate references to multiple different companies' wealth, especially given that the Government's counsel emphasized the wealth of the Harbert companies in his closing statement and insinuated that the money would be in better hands if it were taken from the defendants. We therefore vacate the judgments with respect to HII and HC and remand for a new trial for those two defendants.

H. Sufficiency of the Evidence
Finally, the defendants argue that the evidence was insufficient to support the jury verdict. Given our resolution of the foregoing issues, however, we need address only the arguments made by HUK and BIE. See Part II.D (claims against Anderson, which were limited to Contract 29, are time-barred); Part II.E (Government's contradiction of stipulation regarding BHIC requires new trial); Part II.G.4 (evidence of HII and HC's wealth requires new trial).
The jury found HUK liable for conspiracy, as well as for substantive FCA violations *899 with respect to Contract 20A. To hold HUK liable for conspiracy, the jury must have found (1) that an agreement existed to have false or fraudulent claims allowed or paid by the United States; (2) that HUK willfully joined that agreement, either at the conspiracy's inception or afterwards; and (3) that one or more conspirators knowingly committed one or more overt acts in furtherance of the object of the conspiracy. See Miller v. Holzmann, 563 F.Supp.2d 54, 114 n. 83 (D.D.C.2008); see also, e.g., Halberstam v. Welch, 705 F.2d 472, 478 (D.C.Cir.1983) (describing the elements of common law civil conspiracy). HUK challenges all three findings. Although estopped from challenging its liability, see Part II.F, BIE joins HUK in contending that the jury erred in its calculation of damages.
The district court denied the defendants' motion for judgment as a matter of law with respect to the sufficiency of the evidence. Although we review that decision de novo, we "do not .. . lightly disturb a jury verdict." McGill v. Muñoz, 203 F.3d 843, 845 (D.C.Cir.2000). We "draw all reasonable inferences in favor of the nonmoving party and ... may not make credibility determinations or weigh the evidence." Reeves v. Sanderson Plumbing Prods., Inc., 530 U.S. 133, 150, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000). We "disregard all evidence favorable to the moving party [here, the defendants] that the jury is not required to believe," id. at 151, 120 S.Ct. 2097, and will reverse a jury's decision "only if the evidence and all reasonable inferences that can be drawn therefrom are so one-sided that reasonable men and women could not have reached a verdict in plaintiff[s'] favor." McGill, 203 F.3d at 845 (internal quotation marks omitted).

1. Overarching Conspiracy
The plaintiffs alleged and the jury found an overarching conspiracy spanning Contracts 20A, 29, and 07. HUK contends that the evidence does not support this finding and that we must therefore reverse both the conspiracy and substantive verdicts against it. We must reverse the conspiracy verdict, HUK urges, because record evidence shows only that Peter Schmidt "was involved in three separate and distinct episodes of discussing bid-rigging." Citing Kotteakos v. United States, 328 U.S. 750, 774, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946), the defendants also argue that we must reverse the substantive verdict because the overarching conspiracy theory created "dangers of transference of guilt from one [defendant] to another." In other words, HUK argues, the jury may well have relied on its conspiracy verdict to hold HUK liable for substantive FCA violations based on the actions of its co-conspirators. See Halberstam, 705 F.2d at 481.
As we explained in United States v. Tarantino, 846 F.2d 1384, 1393 (D.C.Cir.1988), a jury must consider three factors to determine whether potentially connected conduct constitutes an overarching conspiracy: (1) "whether the conspirators share[d] a common goal"; (2) "the degree of dependence inherent in the conspiracy"; and (3) "the overlap of participants" between the arguably separate schemes. Pointing out that Tarantino involved a drug conspiracy, HUK argues that this framework is inapplicable, or at least more demanding, where, as here, the conspiracy is of a commercial nature. But we have repeatedly applied this three-part inquiry to non-drug conspiracies without altering its contours. See, e.g., United States v. Hemphill, 514 F.3d 1350, 1363-64 (D.C.Cir.2008) (single conspiracy to steal from Washington Teachers Union); United States v. Gatling, 96 F.3d 1511, 1520 (D.C.Cir.1996) (single conspiracy to commit bribery in connection with illegal issuance of section 8 housing subsidies); cf. *900 United States v. Anderson, 326 F.3d 1319, 1327-28 (11th Cir.2003) (applying this three-part framework and upholding a jury finding of an overarching conspiracy in Anderson's criminal case on the same facts as in the case before us). To apply that test to the overarching conspiracy the jury found in this case, we must consider testimony and evidence regarding the bidding on each contract even though, as explained in Part II.A.2, Contracts 29 and 07, by themselves, cannot give rise to substantive liability against any defendant. Cf. Hemphill, 514 F.3d at 1363-64 (considering evidence relating to multiple schemes as proof of one overarching conspiracy).
In assessing the first factor whether defendants involved in allegedly conspiratorial conduct shared a common goal"a conspiracy's purpose should not be defined in too narrow or specific terms." Gatling, 96 F.3d at 1520. Thus, we have found "obtaining money in exchange for [government] subsidies," id., and "steal[ing] money from [a] union," Hemphill, 514 F.3d at 1364, to be sufficiently specific common purposes. Reviewing the evidence, the district court determined that the jury could have reasonably found an overarching conspiracy with a common purpose of "limiting competition" in bidding on projects in Egypt funded by the USAID. Miller, 563 F.Supp.2d at 138-139 & n. 131. We agree.
The jury heard testimony revealing just such a common purpose, including for example Anderson's statement that all prequalified contractors working in Egypt were part of a "Frankfurt Club" that "set up" the bids on Egyptian contracts. John Ollis, Vice President of Holzmann, inferred from Anderson's comments that "the jobs that we were bidding, there had been some kind of arrangements made among the bidders to collaborate on how much would be bid. In the vernacular, bid-rigging." The defendants contend that even if the other participants shared the common goal of limiting competition in Egypt, "Schmidt had a separate goalpursing Holzmann's interests in Europe." In support, they point to testimony that Schmidt offered to make a trade with SUSA, a prequalified bidder on Contract 29, under which SUSA would win that contract in exchange for Harbert-Jones winning a later contract in Europe. During the second Contract 29 meeting, however, Schmidt abandoned this plan, and in any event, Schmidt's fleeting desire to use the conspiracy to accomplish an additional goal is insufficient to undermine the jury's finding of a common purpose across all three contracts.
The second factor, interdependence, requires that each defendant's actions "facilitate the endeavors of other alleged coconspirators or facilitate the venture as a whole." United States v. Carnagie, 533 F.3d 1231, 1238 (10th Cir.2008) (internal quotation marks omitted); see also Tarantino, 846 F.2d at 1392-93. We have upheld a jury's finding of interdependence where "the assistance one branch of a conspiracy provides to another is fairly minimal" and where "given the overlap in participation and timing ... accusations relating to one of the schemes could trigger an investigation that would lead to exposure" of the others. Gatling, 96 F.3d at 1522. This standard is clearly satisfied here. For one thing, a written bid-rigging agreement between Holzmann and Archirodon (Fuller's parent company) regarding Contract 20A expressly contemplated future collusion on Contract 29. Similarly, a SUSA manager testified that Schmidt offered SUSA a deal in which "the loser" on Contract 29 would bid high on that contract and "the winner" would compensate "the loser" "in kind," by bidding high on another "contract[] to be bid in Egypt similar to [Contract 29]." The jury could also have reasonably inferred interdependence from financial statements for the *901 "Harbert-Jones Egypt Joint Venture," which included Contract 20A, Contract 07, and other projects.
The third factoroverlap among participantsis "less significant" than the others, requiring "only that the main conspirators work with all the participants." Hemphill, 514 F.3d at 1363 (citing United States v. Mathis, 216 F.3d 18, 23-24 (D.C.Cir.2000)). Again, record evidence satisfies this standard. The defendants concede that Schmidt, on behalf of Jones and its parent company, Holzmann, was involved in all three contracts. The jury also heard evidence (1) that another prequalified bidder, Fru-Con (through its parent company, Bilfinger & Berger), received payoffs for cooperating on Contracts 20A and 07; (2) that BIE admitted conspiring to rig bids on Contracts 20A and 29; and (3) that Anderson participated in meetings on Contracts 20A and 07, may well have participated in a meeting on Contract 29, and had authority over all three contracts. Thus, the jury could have reasonably concluded that Schmidt and possibly Anderson worked with all participants and that BIE and HII (through Anderson) were directly involved in rigging bids on multiple contracts. The defendants respond that with the exception of Schmidt and Anderson, each individual met with competitors to discuss but one contract. True enough, but because the conspiracy was between corporations, the identity of the individuals representing those corporations at bid-rigging meetings is irrelevant. In sum, then, sufficient evidence supports the jury's finding of an overarching conspiracy.

2. HUK's Involvement in the Conspiracy
Even if a reasonable jury could have found an overarching conspiracy, HUK insists that the evidence is insufficient to show that it willfully joined that conspiracy. In evaluating this argument, we note that "in most civil conspiracy cases," the jury "ha[s] to infer an agreement from indirect evidence." Halberstam, 705 F.2d at 486. A jury may infer that a defendant willfully joined the conspiracy if he understood the scheme's "essential nature and general scope." Hobson v. Wilson, 737 F.2d 1, 52 (D.C.Cir. 1984) (internal quotation marks omitted), overruled in part on other grounds by Leatherman v. Tarrant County Narcotics Intelligence & Coordination Unit, 507 U.S. 163, 113 S.Ct. 1160, 122 L.Ed.2d 517 (1993). Under basic principles of agency law, corporate defendants are charged with constructive knowledge of all material facts that their agents and officers learn in the scope of their employment. See 2 William Fletcher, Cyclopedia of the Law of Corporations § 790 (2010); see also BCCI Holdings (Luxembourg), S.A. v. Clifford, 964 F.Supp. 468, 478 (D.D.C.1997). Thus, to uphold the jury's finding that HUK joined the conspiracy, we must be sure that the record contains sufficient evidence for the jury to have reasonably found that (1) an HUK employee, officer, or director knowingly joined the conspiracy and (2) in so doing, acted within the scope of his HUK duties.
At trial, the plaintiffs presented testimony and evidence that revealed HUK's involvement in bidding on Contract 20A. In April 1988, the USAID and an Egyptian government agency called the Cairo Wastewater Organization solicited bids on Contract 20A from three prequalified contractors: George A. Fuller Co. (Fuller); Fru-Con Construction Company; and the Harbert-Jones 20A Joint Venture.
A month later, Schmidt invited a group of prequalified contractors to meet in Frankfurt. Schmidt suggested that the others bid high on Contract 20A in exchange for a payoff. Although no agreement was reached at that meeting, several *902 weeks later Schmidt and an executive of Bilfinger & Berger (B & B) (Fru-Con's parent company) agreed that Fru-Con would submit a high bid in exchange for a payoff equivalent to 2-3% of the contract value.
The Harbert-Jones joint venture convened a bid reconciliation meeting in June. Jones's estimator, Carl Nagel, proposed that Harbert-Jones bid $95.2 million. Ian Young, HUK's lead estimator, represented Harbert at the meeting, where the Harbert team suggested to the Jones team that they include more conservative estimates. Based in part on these suggestions, the two sides initially agreed to bid $103 million. After Anderson arrived at the meeting and once additional "philosophy changes," including more expensive methods of construction, were incorporated into the bid, the joint proposal increased to $130 million. Shortly thereafter, Harbert-Jones submitted a $125 million bid, which Young signed.
On August 3, the final day to submit bids, Schmidt and an officer of Fuller's parent, Archirodon, signed a written agreement stipulating that Fuller would refrain from bidding on Contract 20A in exchange for Archirodon receiving either 5% of the contract value or 3% and a subcontract. In addition, Holzmann committed to "caus[ing]" Harbert-Jones to "reciprocate" by helping Fuller obtain another contract of similar value from the USAID, such as Contract 29. On the same day, Young directed that the Harbert-Jones bid be increased by 3.5%, to $129 million.
The bids were opened the next day. Fru-Con had bid $152 million, Harbert-Jones had bid $129 million, and Fuller had not bid at all. Although the lower of the bids, Harbert-Jones's was substantially higher than the project's consultant had expected. As a result, the Cairo Wastewater Organization and the USAID opted to scale down the contract and solicit re-bids.
In December, Anderson, Schmidt, and Archirodon representatives met to discuss the new round of bidding. In a handwritten addendum to the August agreement, they agreed that Fuller would receive a subcontract worth at least $2.5 million plus $500,000 cash. Later that month, Fru-Con bid $139 million for the scaled-down version of Contract 20A, and Harbert-Jones bid $115 million. Harbert-Jones won the contract, eventually submitting 33 invoices totaling over $107 million.
In January 1990, Schmidt, Anderson, and a representative from Archirodon negotiated a payment schedule for the agreed-upon $3 million payoff. Holzmann made payments to Archirodon over the next year. Testimony and other evidence suggest that Harbert-Jones funneled money for these payoffs through HUK. For example, Holzmann billed HUK for services it never requested nor received, and HUK paid those invoices.
According to HUK, this evidence is insufficient to support the jury's finding that the company agreed to join the overarching conspiracy. We disagree. The jury could have reasonably concluded that Ian Young, HUK's lead estimator, knowingly joined the conspiracy on behalf of HUK. Specifically, Young's interactions with Roy Anderson, his behavior at the Harbert-Jones bid-reconciliation meeting, and his involvement in increasing the bid on the same day that Schmidt secured Archirodon's no-bid promise all suggest he knowingly joined the conspiracy while acting within the scope of his employment for HUK.
The jury had reason to believe that Anderson knew of the conspiracy by the time of the June 1988 bid-reconciliation meeting. Specifically, it heard testimony and viewed evidence that Anderson was *903 the Vice President of HII, the 60% partner in the joint venture; that he was the "lead man" on the Egypt jobs; that he held powers of attorney from the President of HII, Bill Harbert, authorizing him "without reservation" to represent HII in the bidding; and that he may have been present at the May 1988 meeting in which Schmidt proposed the bid-rigging scheme, see Miller, 563 F.Supp.2d at 116 n. 87 ("In light of Anderson's explicit status as HII's point-man in Europe for international contracting and his attendance at the December 1988 renegotiation with Fuller, it would be reasonable to infer that if a HII representative attended the May meeting, it would have been Anderson."). The jury also heard evidence suggesting that Anderson could have passed his knowledge along to Young: Colin Towsey, the Managing Director of HUK, testified that Anderson and Young "had interactions ... with respect to the bidding on Contract 20A," and "had discussions about what the estimating work would be."
In addition, the jury could have reasonably inferred that Young knew of the conspiracy based on evidence that he sought to increase the bid at the Harbert-Jones bid reconciliation meeting. Nagel, Jones's estimator, testified that although Jones's pre-meeting proposal was $95.2 million, Young's "arm twist[ing]" "pressured" the Jones team to include more expensive methods of construction, thus significantly increasing the bid, first to $103 million and later, after Anderson's arrival, to $130 million. Nagel testified that he thought that even the $103 million figure was "inflated." According to Nagel, the Jones team deferred to Young because Harbert was the majority owner of the joint venture, giving Harbert "the hammer" in the negotiations. Similarly, Young's August 3 order to increase the bid by 3.5%the same day Schmidt secured a no-bid agreement from Archirodoncould also lead a reasonable jury to conclude that he knew about the bid rigging. Reinforcing these inferences, the plaintiffs' expert explained that in order to make collusive agreements profitable, managers must exert influence on the prices their companies set.
HUK challenges this view of the evidence, arguing that an innocent explanation supports Young's actions and that "[c]onduct that is as consistent with other equally plausible explanations as with illegal conspiracy, without more, does not support an inference of conspiracy." See Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986); Monsanto Co. v. Spray-Rite Serv. Corp., 465 U.S. 752, 768, 104 S.Ct. 1464, 79 L.Ed.2d 775 (1984). According to HUK, at the bid-reconciliation meeting Young simply believed that more conservative construction techniques should be used. This explanation is bolstered, HUK tells us, by Nagel's statement on cross-examination that reasonable and experienced estimators could disagree about the need for such methods. Similarly, HUK contends that Young's August 3 order to increase the bid by 3.5% was completely innocentthe letter was one of two prepared in advance to deal with volatile steel prices. As the district court observed, however, these arguments largely ignore the standard of review for sufficiency challenges: "In essence, HUK merely posits that anotherin its opinion, betterexplanation of the facts exists. But at this stage in the litigation, the relevant question is whether the view adopted by the jury in reaching its verdict was at all reasonable." Miller, 563 F.Supp.2d at 121 n. 98 (citing Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 251, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986)). Here the jury had sufficient evidence to conclude that Young's efforts to increase the bid were motivated by knowledge of a bid-rigging conspiracy. Moreover, in crediting the plaintiffs' version of the facts over *904 HUK's more innocent explanation, the jury would have had no need to speculate, as HUK claims it did. Testimony regarding Young's interactions with Anderson, the existence of a bid-rigging agreement between Harbert-Jones and Fru-Con, the timing of Young's actions, and the expert testimony about collusive agreements all support the jury's inference that Young knowingly joined the conspiracy. Cf. Matsushita, 475 U.S. at 596-97, 106 S.Ct. 1348 (where plaintiffs fail to show that defendants had any plausible motive to engage in conspiracy, conduct consistent with other, equally plausible explanations does not give rise to an inference of conspiracy).
Sufficient evidence also supports the jury's finding that Young acquired knowledge of the conspiracy while acting within the scope of his employment for HUK. Not only was Young an HUK employee when Contract 20A was bid, but in his testimony, Colin Towsey, HUK's Managing Director, revealed that Young worked on the bid as part of his HUK employment. HUK counters that Towsey's testimony suggests that during the relevant period Young was actually working for BIE, HUK's 49% owner. But Towsey's testimony establishes only that HUK "provide[d] some engineering and estimating support" to BIE. Towsey never said that Young worked primarily or exclusively for BIE; in fact, Towsey indicated that Young worked in HUK's London office during this time, that he remained on HUK's payroll, and that "[h]e was certainly the head of [HUK's] estimating team" in connection with Contract 20A. Thus, based on Towsey's testimony the jury could have reasonably found that Young learned of the conspiracy and contributed to it in his capacity as an HUK employee. In sum, then, Young's actions provided sufficient evidence for the jury to conclude that HUK knowingly joined the conspiracy.
HUK next challenges the jury's finding that it committed substantive FCA violations, i.e., that it "knowingly present[ed], or cause[d] to be presented, a false or fraudulent claim" and "knowingly ma[de], use[d], or cause[d] to be made or used, a false record or statement material to a false or fraudulent claim" with respect to Contract 20A. 31 U.S.C. § 3729(a). We have no need to address this argument. Because the jury had sufficient evidence to find that HUK conspired to submit false bids, supra at 58, HUK was liable for its co-conspirators' foreseeable actions in support of the conspiracy. See, e.g., Halberstam, 705 F.2d at 481. And as explained in Part II.G.1, BIE's admission that it both conspired to and did submit false claims with respect to Contract 20A was properly admitted against all of the defendants. That admission thus provides sufficient evidence for the jury to have found HUK liable for false claims submitted on Contract 20A. We therefore turn to the defendants' challenges to the jury's calculation of damages.

3. Damages
As the parties agree, the measure of damages is the difference between what the United States paid and what it would have paid had there been no bid-rigging agreement. Because the plaintiffs' claims on Contracts 29 and 07 are barred by the statute of limitations, see Part II.A.2, we need consider damages only as to Contract 20A. After being instructed on the proper standard, the jury awarded damages of $29.9 million on that contract. HUK and BIE challenge the award on two independent grounds. First, they contend that the plaintiffs presented insufficient evidence to support the jury's finding. Second, they argue that the district court permitted the plaintiffs to argue an improper damages theory to the jury and that this error requires a new trial.
*905 Regarding the sufficiency of the evidence, the defendants assert that "plaintiffs failed altogether to prove that USAID incurred [any] loss" from the bid rigging on Contract 20A. This claim rests on the contention that no defendant attended the bid-rigging meetings led by Schmidt on behalf of Holzmannindeed, that no defendant even knew about the meetings and that Harbert-Jones therefore could not have raised its bid based on Schmidt's agreements with the other Contract 20A bidders. Our earlier discussion explains why this argument fails: a reasonable jury could have concluded that Anderson and Young, representing the Harbert side of the Harbert-Jones venture, knew about the bid-rigging plan when they attended the venture's June 1988 bid-reconciliation meeting and that, based on that knowledge, they aggressively advocated a higher bid.
Moreover, the jury heard substantial evidence that the payment Harbert-Jones ultimately received for its work on Contract 20A was well above what it could have obtained through a competitive bidding process. Although the joint venture's bid rose and fell several times between the June 1988 bid reconciliation meeting and the final award of the contract, in the end, executives at Jones described their profits as "exorbitantly wonderful." Indeed, the plaintiffs' expert testified that Harbert-Jones reaped profits of 52%; other witnesses testified that the norm for construction jobs of this type is 7 to 15%. The plaintiffs' expert also detailed several complicated financial transactions that BIE undertook to hide $25 million of this profit. Contrary to the defendants' argument, it required no speculation for the jury to conclude that the defendants overcharged on Contract 20A.
As to the amount of the award, the defendants argue that even if the plaintiffs successfully proved some degree of bid inflation, "there is no correlation between the $29,920,000 jury award and any of the various amounts plaintiffs urged the jury to assess." When considering a sufficiency of the evidence challenge to a jury's damages award, "[o]ur inquiry ends once we are satisfied that the award is within a reasonable range and that the jury did not engage in speculation or other improper activity." Carter v. Duncan-Huggins, Ltd., 727 F.2d 1225, 1239 (D.C.Cir.1984). Especially in a case like this, "[w]here the jury finds a particular quantum of damages and the trial judge refuses to disturb its findings," we must be "certain indeed that the award is contrary to all reason" before reversing the jury and the district court. Id. (internal quotation marks omitted). And in determining what constitutes a "reasonable range" for the jury's award, we make allowances for the fact that the defendants' own misconduct has foreclosed any exact calculation of what a competitive bid would have been on Contract 20A. See Bigelow v. RKO Radio Pictures, Inc., 327 U.S. 251, 264, 66 S.Ct. 574, 90 L.Ed. 652 (1946) ("[W]here the defendant by his own wrong has prevented a more precise computation, the jury may not render a verdict based on speculation or guesswork[,][b]ut [it] may make a just and reasonable estimate of the damage based on relevant data.").
At trial, the plaintiffs suggested several methods for estimating the extent of the bid inflation on Contract 20A. We highlight two, each of which demonstrates that the jury's award falls "within a reasonable range." Carter, 727 F.2d at 1239.
First, the plaintiffs urged the jury to begin with the defendants' actual final costs on Contract 20A of $52 million, and then add a generous 25% profit margin (as described above, the jury heard testimony that profit on a contract like 20A would normally have been 7 to 15%), thus yielding *906 a final bid of $65 million. Since Harbert-Jones ultimately submitted invoices totaling $107 million, this calculation suggested damages of $42 million ($107 million minus $65 million), comfortably above the jury's actual $29.9 million award.
Alternatively, the plaintiffs suggested that the jury could estimate the competitive bid amount for the final Contract 20A specification by starting with either of two "free of influence" estimates for the original, larger version of the contract, and then discounting whichever estimate it chose for the subsequent scope of work changes. The two estimates the plaintiffs suggested as a baseline were: (1) $95 million, the bid proposal prepared by Jones before its June 1988 reconciliation meeting with the Harbert side of the venture, and (2) $80 million, the bid amount apparently considered by Fuller before deciding not to bid on Contract 20A. Proportionately reduced for the subsequent changes to Contract 20A that led Harbert-Jones to lower its bid from $129 to $115 million (an 11% reduction), these estimates suggest that the competitive bid amount on the final contract would have been between $71 and $85 million, indicating damages of $22 to $36 million. The jury's actual award$29.9 millionfalls squarely within this range. The jury's award thus easily survives our deferential standard of review.
Finally, the defendants argue that the district court allowed the plaintiffs to present an improper damages theory to the jury. Specifically, they contend that by allowing the plaintiffs' counsel to refer occasionally to the proper measure of damages as what the Government "should" have paid rather than what it "would" have paid absent the bid rigging, the district court allowed the plaintiffs to suggest that the jury calculate damages by disgorging the defendants' Contract 20A profits. Cf. United States ex rel. Harrison v. Westinghouse Savannah River Co., 352 F.3d 908, 923 (4th Cir.2003) (finding disgorgement of all government payments on a fraudulently obtained contract to be an inappropriate remedy under the FCA). "[W]here a jury was permitted to consider an improper standard of damages," the defendants argue, "the reviewing court must reverse unless it can be assured that the verdict was not based on [the] erroneous standard." In its post-trial order, however, the district court pointed out that its jury instructions set out the proper damages standard and found that these instructions "eliminated any confusion engendered by plaintiffs' counsel[]." 563 F.Supp.2d at 108 n. 68.
Reviewing the district court's denial of a new trial for abuse of discretion, we find none. To begin with, we doubt very much that the few offhand references to what the Government "should have paid" could have misled the jury. As the plaintiffs point out, "what the Government `should have paid' can readily be understood as what the Government ought to have paid on the contracts absent Defendants' wrongdoing." Indeed, in describing the proper measure of damages in his closing argument, the plaintiffs' counsel used the phrase "should have paid" in just this way: "[T]he measure of the damage will be ... that difference between what [the Government] paid and what [it] should have paid if the bidding had not been rigged and the competition had been free, robust, and vibrant." But even if these scattered "should have paid" references may have confused the jury, we agree with the district court that its instructions eliminated any prejudice. The court explained to the jurors that "the measure of damages to the United States is the difference between what the United States paid and what it would have paid had there been no bid-rigging agreement." As the district court was entitled to presume that the *907 jurors "follow[ed] the instructions they [were] given," United States v. Mouling, 557 F.3d 658, 665 (D.C.Cir.2009), its denial of the defendants' motion for a new trial was well within its discretion.

III. Conclusion
For the foregoing reasons we (1) vacate the judgment of the district court, pursuant to the statute of limitations, with respect to the claims concerning Contracts 07 and 29; (2) vacate the judgment against the defendants HII, HC, and BHIC and remand the matter for a new trial because the district court erred in admitting testimony about the wealth of HII and HC and statements contrary to the stipulation about BHIC's existence; and (3) affirm the judgment with respect to the claims concerning Contract 20A against the remaining defendants, namely BIE and HUK.
So ordered.
TATEL, Circuit Judge, dissenting from Parts II.A.2 and II.G.4:
In Part II.A.2 the court finds the Government's claims on Contracts 29 and 07 barred by the False Claims Act's statute of limitations, and in Part II.G.4 it rules that testimony and evidence regarding the defendants' wealth was so prejudicial as to require a new trial for HII and HC. I respectfully dissent from both rulings.

I
Under the False Claims Act (FCA) as recently amended, the Government's complaint in intervention inherits the filing date of the qui tam relator's complaint that initiated the action "to the extent that the claim of the Government arises out of the conduct, transactions, or occurrences set forth, or attempted to be set forth, in the prior complaint" 31 U.S.C. § 3731(c). In this case, the "conduct, transactions, or occurrences set forth, or attempted to be set forth" in Richard Miller's 1995 complaint involved a Frankfurt-based conspiracy to rig bidding for multiple USAID contracts in Egypt. This court denies relation back of much of the Government's complaint in intervention because two contracts the Government alleges were part of that conspiracy, Contracts 29 and 07, were not mentioned in Miller's original complaint. Yet in the very first sentence in which Miller described the conduct at issue, he left no doubt that he was accusing the defendants of fraud spanning more than one USAID project: "Defendants conspired to rig the bidding for construction contracts paid for by the United States Agency for International Development." Miller Compl. ¶ 1 (emphasis added). Emphasizing that he was alleging fraud involving more than one contract, he continued, "The particular transaction about which most is known is Contract 20A." Id. (emphasis added). After detailing the bid rigging on Contract 20A, id. ¶¶ 1, 15-30, Miller again made clear that the conspiracy he was alleging was not limited to that particular contract: "Plaintiff has received information that there was a `club' in Frankfurt, Germany of contractors qualified to perform AID contracts in Egypt; the club was organized to control prices in what should have been full and open competition for AID contracts." Id. at ¶ 33. Indeed, Miller predicted that discovery would uncover additional rigged contracts: "Upon information and belief, discovery in this case will reveal that other AID contracts in Egypt were subject to similar and related collusive agreements on price that resulted in the submission of other false or fraudulent claims to the U.S. Government." Id. Finally, in the complaint's formal counts, Miller neither mentioned Contract 20A nor limited his claim for damages to the allegedly false claims on that contract (estimated earlier in the complaint at $40 million). Instead, he "incorporate[d] the allegations *908 of" the preceding paragraphs by reference, id. ¶¶ 34, 37, including the allegation of "other false or fraudulent claims" arising from "other AID contracts in Egypt," id. at ¶ 33, and sought "actual damages in an amount to be proven at trial," id. ¶¶ 36, 39.
From the face of Miller's complaint, it is thus clear that the "conduct, transactions, or occurrences set forth, or attempted to be set forth" encompassed bid-rigging not just on Contract 20A (identified by Miller in his original complaint) but also on Contracts 29 and 07 (later added by the Government in its complaint in intervention). The Government's claims on Contracts 29 and 07 "arise[] out of" the Frankfurt-based bid rigging conspiracy originally alleged by Millerindeed, the "collusive agreements" on these contracts were precisely what Miller predicted discovery would unearth. Id. ¶ 33. For this reason, the Government's claims relate back to Miller's original complaint and are therefore not barred by the FCA's statute of limitations. As we have said, "an amendment offered for the purpose of adding to or amplifying the facts already alleged in support of a particular claim may relate back." United States v. Hicks, 283 F.3d 380, 388 (D.C.Cir.2002).
According to the court, "[a]llegations concerning Contract 20A do not fairly encompass Contracts 07 or 29 because each contract is unique." Ct. Op. at 882. In support, it says that "each contract required work to be performed on a different project and was awarded in a different year to a different winning bidder drawn from a different pool of prequalified bidders." Id. This misses the point. Of course the three contracts were different. As is typical in government contracting, USAID and the Egyptian government divided the sewer improvements into multiple contracts signed on different dates. What matters for relation back purposes is that the three contracts were all part of the "conduct," i.e., the Frankfurt-based bid-rigging conspiracy, alleged in Miller's original complaint.
The three contracts, moreover, are not nearly as different as the court suggests. Although each contract was awarded to a "different winning bidder," id., the winners on Contracts 20A and 07 were identical in structureeach was owned 60% by HII and 40% by Jonesand the defendants' financial statements treated them as a single entity, the "Harbert-Jones Egypt Joint Venture." Indeed, had Holzmann not agreed that Harbert-Jones would overbid the contract in exchange for a $4 million loser's fee from its competitor, HII and Jones might have won Contract 29 as well. Moreover, while it is true that the pool of bidders varied among contracts, there were important overlaps: HII and Jones, through their joint ventures, were prequalified to bid on all three, and Fru-Con was prequalified for Contracts 20A and 07. Indeed, "Fru-Con (through its parent company, Bilfinger & Berger), received payoffs for cooperating on Contracts 20A and 07," Ct. Op. at 901. In addition, Fuller, which was prequalified for Contract 20A, also submitted prequalification information on Contract 29 but was ultimately found ineligible. And when Fuller's parent corporation and Holzmann rigged the bidding on Contract 20A, they signed an agreement "expressly contemplat[ing] future collusion on Contract 29." Id. at 900.
The court relies on Meijer, Inc. v. Biovail Corp., 533 F.3d 857 (D.C.Cir.2008), but that case is very different from this one. There, a group of wholesale drug purchasers alleged that Biovail, a drug manufacturer, misused a patent it owned to keep "generic versions" of one of its brand name drugs off the market. The complaint named one particular generic competitor, developed by a company called *909 Andrx, that Biovail had blocked. Id. at 866. In their amended complaint, the plaintiffs alleged for the first time that Biovail, along with its exclusive distributor, Forest Laboratories, also violated the antitrust laws through their "decision not to sell their own generic." Id. (emphasis added). We disallowed relation back of this new allegation even though the original complaint accused the defendants of blocking "generic versions" of the drug. Id. (emphasis added). According to my colleagues, Miller's use of the plural"Defendants conspired to rig the bidding for construction contracts," Miller Compl. ¶ 1likewise cannot support relation back of the Government's subsequent allegations.
Our decision in Meijer, however, rested on the fact that "the whole thrust of the amendments [was] to fault both Biovail and Forest ... for conduct different from that identified in the original complaint." Meijer, 533 F.3d at 866. As we interpreted the plaintiffs' original complaint, it alleged that Biovail, acting alone through misuse of its patent, was "bent upon preventing the FDA from granting final approval of the generic drug proposed by Andrx (and perhaps others)." Id. The plaintiffs' amended complaint, however, differed in two important respects. First, it added claims against Forest, "alleg[ing] for the first time that Biovail and Forest unlawfully conspired to extend their lawful monopoly." Id. Second, it alleged an entirely different means of unlawful monopolization, i.e., that Biovail and Forest "planned preemptively to introduce their own generic Diltiazem HCl, and that they unlawfully abandoned that plan." Id. Thus, our decision in Meijer flowed from the well established principle that "an amendment ... that attempts to introduce a new legal theory based on facts different from those underlying the timely claims may not" relate back. Hicks, 283 F.3d at 388.
Here by contrast the Government's theory of liability on Contracts 29 and 07 is identical to that first pleaded by Miller, namely that the defendants entered into a Frankfurt-based conspiracy to rig the bidding on USAID contracts in Egypt, and that through that conspiracy, the defendants rigged the bidding not just on Contract 20A, but also on Contracts 29 and 07. Indeed, in Meijer we suggested that relation back may well have been appropriate had the plaintiffs therelike the Government heresimply added additional examples of the unlawful conduct alleged in the original complaint. 533 F.3d at 866 (describing plaintiffs' original allegations regarding "generic versions" of Biovail's drug as encompassing "the generic drug proposed by Andrx (and perhaps others)" (emphasis added)).
My colleagues also rely on Bell Atlantic Corp. v. Twombly, 550 U.S. 544, 557, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007), and Ashcroft v. Iqbal, ___ U.S. ___, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009), in which the Supreme Court held that to survive a motion to dismiss, a complaint must provide more than "`naked assertion[s]' devoid of `further factual enhancement.'" Id. at 1949 (quoting Twombly, 550 U.S. at 557, 127 S.Ct. 1955). Characterizing Miller's conspiracy allegation as such an assertion, the court concludes that it cannot support relation back of the Government's claims on Contracts 29 and 07. This argument suffers from two fundamental defects. To begin with, the defendants raised it neither here nor in the district court, and as we have repeatedly said, "appellate courts do not sit as self-directed boards of legal inquiry and research, but essentially as arbiters of legal questions presented and argued by the parties before them." Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983). Second, and setting aside the fact that the allegations in Miller's original complaint, which identified the *910 conspiracy as based in Frankfurt, described the scope of its operations (USAID contracts in Egypt), and detailed its bid-rigging on Contract 20A, are a far cry from the "naked assertions" that doomed the complaints in Twombly and Iqbal, those two cases have no applicability to the question before us. In Twombly and Iqbal the Supreme Court interpreted Federal Rule of Civil Procedure 8(a)(2), which sets the standard that a complaint must satisfy to survive a motion to dismiss. Nothing in either case even hints that the Supreme Court intended Rule 8(a)'s standards to apply to relation back, which is governed by the entirely different language of Rule 15(c), now incorporated into the FCA. In fact, my colleagues' invocation of Twombly and Iqbal contradicts the FCA's plain text, which provides that claims relate back not only to "conduct, transactions, or occurrences set forth," in an earlier complaint, but also to "conduct, transactions, or occurrences ... attempted to be set forth." 31 U.S.C. § 3731(c) (emphasis added); cf. Krupski v. Costa Crociere S.p.A., 560 U.S. ___, 130 S.Ct. 2485, 2496, ___ L.Ed.2d ___, (2010) (emphasizing, with respect to relation back of parties, that Rule 15 "plainly sets forth an exclusive list of requirements for relation back," and "mandates relation back once the Rule's requirements are satisfied" (emphasis added)). Indeed, two other circuits have expressly held, in language we have cited with approval, that an "amended claim arises from the same conduct and occurrences upon which the original claim was based," and therefore relates back, even if (unlike here) "the original claim contained insufficient facts to support it." Dean v. United States, 278 F.3d 1218, 1222 (11th Cir.2002); see also id. ("One purpose of an amended claim is to fill in facts missing from the original claim."); United States v. Thomas, 221 F.3d 430, 436 (3d Cir.2000) (an amendment that "seeks to correct a pleading deficiency by expanding the facts but not the claims alleged" in an earlier filing "would clearly fall within Rule 15(c)"); Hicks, 283 F.3d at 388 (quoting Dean and Thomas). In FCA cases, the time for defendants to file Iqbal motions, and thus to ensure that Rule 8(a)'s pleading standards are not "circumvent[ed]," Ct. Op. 882, is when the relator's complaint is unsealed. And where, as here, the Government files a complaint in intervention and the relator an amended complaint, it is those two complaints, not the relator's initial, sealed complaint, that are tested against the Iqbal standard.
When Miller filed his 1995 complaint, he knew that contracts other than 20A were involved in the Frankfurt Club conspiracy. Congress added the relation back provision to the FCA precisely for situations like thisto allow "a complete and thorough investigation of the merits of a qui tam relators' allegations." S.Rep. No. 110-507, at 28.29 (2008) (report on the False Claims Correction Act of 2008, a FERA predecessor). By interpreting Miller's complaint as limited to the one contract he was able to identify by number when he first filed, and by applying Twombly and Iqbal to Miller's original, sealed complaint, this court deprives the Government of the fruits of just such an investigation and frustrates congressional intent.

II.
After the jury returned its verdict, HII and HC sought a new trial, arguing that the plaintiffs' counsel's questioning of one witness, together with his closing argument, introduced unfairly prejudicial evidence about the defendants' wealth. The district court found that much of the wealth evidence was relevant and that in any event, it was not so prejudicial as to require a new trial. Miller v. Holzmann, 563 F.Supp.2d 54, 110-13; see Fed. R.Civ.P. 61 (all trial errors are harmless *911 unless they affect "substantial rights"). This court now finds that the district court abused its discretion in failing to order a new trial for HII and HC. I cannot agree. Faced with "only a cold record," Edwards v. Sears, Roebuck & Co., 512 F.2d 276, 281 (5th Cir.1975), I would defer to the judgment of the experienced district judge who conducted this seven-week trial and observed the witnesses.
The plaintiffs' counsel elicited information from Raymond Harbert about the assets and structure of HII, HC, and non-party Harbert Management Company. The district court found this testimonyat least with respect to HII and HCrelevant to the Government's alter ego theory, i.e., its argument that as HII's parent, HC completely controlled HII and ignored its separate corporate existence, making it responsible for HII's actions. The district court grounded its relevance finding in circuit precedent establishing that the undercapitalization of a subsidiary corporation may suggest the existence of just such an improper relationship. Miller, 563 F.Supp.2d at 111 (discussing Labadie Coal Co. v. Black, 672 F.2d 92 (D.C.Cir.1982)). In other words, according to the district court, Raymond Harbert's testimony was relevant because it could have suggested to the jury that adherence to the corporate form might have permitted HC "to evade the impact of a judgment against an inadequately capitalized HII." Id.
Having found some of Raymond Harbert's testimony relevant, the district court applied Federal Rule of Evidence 403, asking whether the testimony presented a risk of unfair prejudice that substantially outweighed its probative value. Although recognizing that "knowledge that a defendant has the resources to pay a judgment may increase jurors' comfort level in making a large damages award," the district court found that "a bare handful of remarks in the course of a seven-week trial" fell short of "creat[ing] such unfair prejudice as to substantially outweigh the significant probative value" of the evidence. Id. at 112. A new trial was unnecessary, the district court explained, because "plaintiffs here never even approached the sort of egregious misconduct and overt pandering that have compelled reversal or a new trial in other cases." Id.
With little explanation, this court now rejects the district court's relevance analysis. Ct. Op. at 897-98. More troubling, the court disregards the district court's determination of prejudice. But even if, as this court finds, much of the wealth testimony was in fact irrelevant, we owe substantial deference to the district court's determination that the testimony was not so prejudicial as to "affect ... substantial rights." Fed.R.Civ.P. 61. Indeed, because we have long recognized that the district court's proximity to the trial places it in a far better position to determine prejudice, "[w]e review a trial court's evidentiary rulings for abuse of discretion . . . [and][e]ven if we find error, we will not reverse an otherwise valid judgment unless appellant demonstrates that such error affected her `substantial rights.'" Whitbeck v. Vital Signs, Inc., 159 F.3d 1369, 1372 (D.C.Cir.1998) (citations omitted).
Given that the trial lasted for seven weeks, that the evidence was hardly close, and that the court points to only one series of questions and a single comment in which the defendants' wealth was raised, I cannot say that the district court abused its discretion in refusing to order a new trial. See, e.g., United States v. Mejia, 597 F.3d 1329, 1342 (D.C.Cir.2010) ("embellishment" in prosecutor's closing argument did not require a new trial "where the statement was isolated and the case was not close"). Although my colleagues may well be correct that "[e]vidence need not be reinforced and reiterated again and again *912 for it to be prejudicial enough to warrant a new trial," Ct. Op. at 898, such limited evidence does tend to suggest limited prejudice. Cf. Koufakis v. Carvel, 425 F.2d 892, 901-05 (2d Cir.1970) (district court's refusal to order a new trial constituted an abuse of discretion where counsel made inappropriate comments "[t]hroughout his presentation at trial and in summation," including "many references" likening defendant to a Mafia boss; engaged in "repeated name-calling, such as referring to [defendant] ... as `liar,' `faker,' `phony,' and `perjurious'"; and made it a "theme[]" throughout trial "that the case was one which pitted a `little' and virtuous man of modest resources against a powerful and unscrupulous man with untold wealth."). Because the district court was in a far better position than we to weigh the evidence and determine its effect on substantial rights, I would defer to its judgment.

III.
For the foregoing reasons, I would affirm the district court's ruling that the Government's claims on Contracts 29 and 07 relate back to Miller's 1995 complaint, as well as its finding that the plaintiffs' references to wealth do not require a new trial. And because I agree with the remainder of the district court's rulings, substantially for the reasons given, I would affirm as to all three contracts and, except for BHIC, see Ct. Op. at 888-90, as to all defendants.
NOTES
[1]  In a post-argument letter to the court, the Government belatedly argues at least one claim concerning Contract 29 was timely without regard to relation back because the underlying events occurred less than six years before the Government filed its Complaint in Intervention. Because the Government failed to raise this point in the district court or in its briefs in this court, the point is doubly forfeit and we do not consider it. See Bryant v. Gates, 532 F.3d 888, 898 (D.C.Cir.2008). With the exception of the arguments regarding recent decisions of the Supreme Court, the same is true for the other arguments the parties raised in the various post-argument letters. See id.; Fed. R.App. P. 28(j).
[2]  Although the defendants were aware of the criminal investigation involving the same conduct, they did not have notice until 2001 of the precise allegations in the Government's FCA complaint.
[3]  The parties agree this is the complaint to which BIE should have referred in order to determine the identity of the intended defendant. BIE states, "Similar allegations appear in the government's Complaint in Intervention," and does not identify any significant differences between the complaints for these purposes.
[4]  Crociera means cruise in Italian. See Krupski, 560 U.S. at ___, 130 S.Ct. at 2498.
[5]  In a footnote, the plaintiffs also cite two other statements to support their assertion that HII and HC brought up their wealth "throughout trial." The first reference only obliquely touches on those companies' wealth when counsel asked Miller about wealthy corporations in general. Nothing was said about HII or HC in particular. The second reference is even less pertinent. There, counsel asked a witness if she thought John Harbert, Bill Harbert's nephew who was also involved in the Harbert companies, ever "felt that he needed to investigate or look over the shoulder of Mr. Bill Harbert." In response, the witness testified the two might have been a little suspicious of each other and recalled that John Harbert spent a lot of money on his hunting dogs. Whatever insight that testimony gave into the relationship between those two men, it had nothing to do with HII and HC's wealth.
