
554 F.3d 300 (2009)
In re AMERICAN EXPRESS MERCHANTS' LITIGATION. *301 
Italian Colors Restaurant, on or behalf of itself and all similarly situated persons, National Supermarkets Association, 492 Supermarket Corp., Bunda Starr Corp., Phoung Corp., Plaintiffs-Appellants,
v.
American Express Travel Related Services Company, American Express Company, Defendants-Appellees.
Docket No. 06-1871-cv.
United States Court of Appeals, Second Circuit.
Argued: December 10, 2007.
Decided: January 30, 2009.
Gary B. Friedman, Friedman Law Group LLP (Tracey Kitzman, Aaron Patton, Warren Parrino, on the brief), Blaine H. Bortnick, Christine Palmieri, Liddle & Robinson, L.L.P., Noah Shube, Law Offices of Noah Shube, Bernard Persky, Eric Belfi, Labaton Sucharow & Rudoff LLP, Brian Brooks, Murray, Frank & Sailer LLP, Curtis V. Trinko, Law Offices of Curtis V. Trinko LLP, Paul C. Whalen, Whalen & Tusa, PC, New York, NY, Read K. McCaffey, Christopher W. Hellmich, Patton Boggs LLP, Roy A. Katriel, The Katriel Law Firm, PLLC, Washington, DC, Mark Reinhardt, Mark Wendorf. Reinhardt Wendorf & Blanchfield, St. Paul. MN, Robert W. Cohen, Law Offices of Robert W. Cohen, Los Angeles, CA, David Markun, Edward Zusman, Kevin Eng, Markun Zusman & Compton LLP, Robert C. Schubert, Willem F. Jonckheer, Schubert *302 & Reed LLP, Susan G. Kupfer, Glancy Binkow & Goldberg LLP, San Francisco, CA, Karl Cambronne, Jefrey D. Bores, Chestnut & Cambronne P.A., Minneapolis, MN, Michael Goldberg, Glancy Binkow & Goldberg LLP, Los Angeles, CA, for Plaintiffs-Appellants.
Bruce H. Schneider, Stroock & Stroock & Lavan, LLP (Heidi Balk, on the brief), Jonathan M. Jacobson, Wilson Sonsini Goodrich & Rosati, Evan R. Chesler, Cravath, Swaine & Moore LLP, Stuart A. Alderoty, American Express Travel Related Services, Inc., New York, NY, Julia B. Strickland, Stephen J. Newman, Stroock & Stroock & Lavan LLP, Los Angeles, CA, for Defendants-Appellees.
Janet L. McDavid, Catherine E. Stetson, Jake M. Shields, Hogan & Hartson L.L.P. (Maria Ghazal, Business Roundtable, of counsel), Washington, DC, for Business Roundtable, Amici.
Briscoe R. Smith, Martin S. Kaufman, New York, NY, for Atlantic Legal Foundation, Amici.
Daniel E. Gustafson, Karla M. Gluek, Gustafson Gluek PLLC, Minnesota, MN, for American Antitrust Institute, Amici.
Edith M. Kallas, Ilze C. Thielmann, Joy A. Nesbitt, Whatley Drake & Kallas LLC; Steven E. Fineman, Jennifer Gross, Lieff Cabraser Heimann & Bernstein, LLP, New York, NY; F. Paul Bland, Jr., Trial Lawyers for Public Justice, Washington DC, for Trial Lawyers for Public Justice, Amici.
POOLER, SACK, and SOTOMAYOR, Circuit Judges.
POOLER, Circuit Judge:
This Court frequently enforces mandatory arbitration clauses contained in commercial contracts. We do so on the principle that "it is difficult to overstate the strong federal policy in favor of arbitration, and it is a policy we have often and emphatically applied." Arciniaga v. General Motors Corp., 460 F.3d 231, 234 (2d Cir.2006) (quotation marks omitted). On this appeal, however, we are asked to consider the enforcement of a mandatory arbitration clause in a commercial contract that also contains a "class action waiver," also referred to as a "collective action waiver," that is, a provision which forbids the parties to the contract from pursuing anything other than individual claims in the arbitral forum. This is a matter of first impression in our Court.[1]
*303 One commentator has recently contended that "[t]he outright banning of class action in mandatory arbitration clauses has become a standard policy for many corporations that transact with consumers." Bryan Allen Rice, "Comment: Enforceable or Not?: Class Action Waivers in Mandatory Arbitration Clauses and the Need for a Judicial Standard," 45 Hous. L.Rev. 215, 224 (2008).[2] We acknowledge at the outset, as have other courts that have considered questions arising from the enforcement of class action waivers, in both consumer and commercial contracts, that the wisdom and utility of these provisions have become the subject of intense debate. See Skirchak v. Dynamics Research Corp., 508 F.3d 49, 63 (1st Cir.2007) ("We recognize that there is a policy debate about whether class action waivers essentially act as exculpatory clauses, allowing for violations of laws where individual cases involve low dollar amounts and so will not adequately address or prevent illegality."). The opposing positions in this frequently impassioned debate have been dispassionately described as follows:
Companies' use of class action waivers is motivated by the view that plaintiffs exploit the class action procedure in order to wrest large and unfair settlements from defendants.... Class action waivers are viewed by these companies as a way to defend themselves from consumers who are ganging up on companies through the leverage inherent in the aggregation of large numbers of claims. In further support of these waivers, corporations argue that the many (perceived) advantages of arbitration to a plaintiff make up for any disadvantages or inconveniences that the plaintiff may incur by sacrificing the ability to be part of a class action.
... Opponents of class action waivers contend that the ability to aggregate claims is crucial to protect the rights of those individuals ... who do not have the resources to litigate individual claims. Further, many individual claims are only viable if brought on a class-wide basis. Indeed, by prohibiting class actions in ... lawsuits[ ] where the expected recovery is dwarfed by the cost of litigating or arbitrating the claim, individuals are effectively prevented from pursuing their claims. As a result, businesses are able to engage in unchecked market misbehavior....
J. Maria Glover, "Beyond Unconscionability: Class Action Waivers and Mandatory Arbitration Agreements," 59 Vand. L.Rev. 1735, 1746-47 (2006) (footnotes and internal quotation marks omitted).
*304 Both of these positions have been proffered to the Court by amici. Compare Brief of Atlantic Legal Foundation at 4 ("For several decades, providers of products and services in the United States have been beset with a litigious environment that has evoked criticism of many observers and applauded only by those professionals who have harvested the substantial financial rewards the civil justice system has produced by way of attorneys' fees.... Recognizing the risks of defending against class action litigation, many businesses have elected to have disputes resolved by individual arbitrations and to adopt collective action waivers as part of their arbitration clauses with their business customers to insure that result.") with Brief of Trial Lawyers for Public Justice at 27 ("It is ... crucial to understand that any ban on class arbitration is essentially a ban on class treatment altogether, as arbitration clauses in standardized corporate contracts are made broader and broader, to encompass all conceivable types of disputes.... Under a regime where such prohibitions are enforced, such clauses are tantamount to a clause banning all claims against a corporation, unless they are so large that they justify the outlay of the extraordinary expense involved.").[3]
We note that two standard treatises on the conduct of class action litigation appear to take opposing positions as well. Compare 1 Joseph M. McLaughlin, McLaughlin on Class Actions: Law and Practice, § 2:14 (3d ed. 2006) ("As the potential availability of class-wide arbitration threatens to multiply exponentially the exposure on what is facially a single-consumer issue, companies should strongly consider including in their standard arbitration agreements an express provision barring class action litigation or arbitration.") with 3 Alba Conte & Herbert B. Newberg, Newberg on Class Actions, § 9:67 n. 2 (4th ed. 2008) ("The bar on class arbitration threatens the premise that arbitration can be a fair and adequate mechanism for enforcing statutory rights.").
While we are conscious of this debate, we are thankful that we need not resolve it on this appeal. That is, we do not decide whether class action waiver provisions are either void or enforceable per se. Rather, we are concerned solely with the class action waiver contained in the contract between the parties before us on this appeal. We conclude that, on the record before us, the plaintiffs have adequately demonstrated that the class action waiver provision at issue should not be enforced because enforcement of the clause would effectively preclude any action seeking to vindicate the statutory rights asserted by the plaintiffs.

FACTS
A. Procedural Posture. The plaintiffs appeal from the judgment, dated March 20, 2006, memorializing the memorandum opinion and order, dated March 15, 2006, of the United States District Court of the Southern District of New York, which granted defendants American Express *305 Company and American Express Travel Related Services Company, Inc.'s (collectively "Amex") motion to compel arbitration. See In re American Express Merchants Litig., No. 03cv9592, 2006 WL 662341 (S.D.N.Y. March 16, 2006) (Daniels, J.). The earliest iteration of the plaintiffs' claims was made in August 2003, with the filing of a class action complaint in the United States District Court for the Northern District of California ("the Italian Colors action"). This action, and another subsequently filed class action, were transferred, on Amex's motion, brought pursuant to 28 U.S.C. § 1404(a), to the United States District Court for the Southern District of New York. (JA 14, 85) By an order, dated December 10, 2004, that court consolidated these two actions, pursuant to Rule 42(a) of the Federal Rules of Civil Procedure, with several class actions that had been filed in the Southern District of New York. Any subsequently filed related actions were also made subject to this consolidation order.
Because we consider here only the narrow question of whether the class action waiver provision contained in the contract between the parties should be enforced, a prolix description of the plaintiffs' claims is unnecessary. (And, needless to say, we take no position on the merits of these claims.) In their briefs on this appeal, the parties describe the plaintiffs' claims largely by reference to the amended complaint, filed December 24, 2003, in the Italian Colors action. We will do so as well.
B. The Parties. The plaintiffs allege that Amex "is the leading issuer of general purpose and corporate charge cards to consumers and businesses in the United States and throughout the world. It is also the leading provider of charge card services to merchants." The named plaintiffs are: (1) California and New York corporations which operate businesses which have contracted with Amex and (2) the National Supermarkets Association, Inc. ("NSA"), "a voluntary membership-based trade association that represents the interests of independently owned supermarkets." The named plaintiffs seek to represent the following class, pursuant to Rule 23 of the Federal Rules of Civil Procedure:
The class is comprised of all merchants that have accepted American Express charge cards (including the American Express corporate card), and have thus been forced to agree to accept American Express credit and debit cards, during the longest period of time permitted by the applicable statute of limitations ... throughout the United States....
C. The Card Acceptance Agreement. The basic contractual relationship between Amex and the plaintiffs is set forth in an affidavit of an Amex executive:
American Express issues card products to its cardmembers, which cardmembers then use in making purchases from participating merchants. Participating merchants with annual charge volume expected to be less than $10 million agree that, by submitting charges for payment by American Express, their relationship will be governed by the "Terms and Conditions for American Express© Card Acceptance" ("the Card Acceptance Agreement").[4]
The Card Acceptance Agreement is a standard form contract issued by Amex. It may be terminated by either party "at any time by sending written notice to the other party." Further, Amex reserves the right

*306 to change this Agreement at any time. We will notify you of any change in writing at least ten (10) calendar days in advance. If the changes are unacceptable to you, you may terminate this Agreement as described in the section entitled "TERMINATING THIS AGREEMENT."
According to Amex, the Card Acceptance Agreement has "expressly permitted amendments upon notice" for more than twenty-five years. The Card Acceptance Agreement also contains a choice of law provision designating New York law as governing and, as Amex states, there is no dispute that the agreement "has always" contained this provision.
By contrast, it is only since 1999 that the Card Acceptance Agreement has contained a mandatory arbitration clause. That clause is nothing if not capaciously worded:
For the purpose of this Agreement, Claim means any assertion of a right, dispute or controversy between you and us arising from or relating to this Agreement and/or the relationship resulting from this Agreement. Claim includes claims of every kind and nature including, but not limited to, initial claims, counterclaims, cross-claims and third-party claims and claims based upon contract, tort, intentional tort, statutes, regulations, common law and equity. We shall not elect to use arbitration under this arbitration provision for any individual Claim that you properly file and pursue in a small claims court of your state or municipality so long as the Claim is pending only in that court.
* * *
Any Claim shall be resolved upon the election by you or us, by arbitration pursuant to this arbitration provision and the code of procedure of the national arbitration organization to which the Claim is referred in effect at the time the Claim is filed. Claims shall be referred to the National Arbitration Forum (NAF), JAMS/Endispute (JAMS), or the American Arbitration Association (AAA), as selected by the party electing to use arbitration. If a selection by us of one of these organizations is unacceptable to you, you shall have the right within thirty (30) days after you receive notice of our election to select one of the other organizations listed to serve as arbitrator administrator.
At the heart of the instant appeal is the fact that the Agreement also contains the following provision:
IF ARBITRATION IS CHOSEN BY ANY PARTY WITH RESPECT TO A CLAIM, NEITHER YOU NOR WE WILL HAVE THE RIGHT TO LITIGATE THAT CLAIM IN COURT OR HAVE A JURY TRIAL ON THAT CLAIM.... FURTHER, YOU WILL NOT HAVE THE RIGHT TO PARTICIPATE IN A REPRESENTATIVE CAPACITY OR AS A MEMBER OF ANY CLASS OF CLAIMANTS PERTAINING TO ANY CLAIM SUBJECT TO ARBITRATION. THE ARBITRATOR'S DECISION WILL BE FINAL AND BINDING. NOTE THAT OTHER RIGHTS THAT YOU WOULD HAVE IF YOU WENT TO COURT MAY ALSO NOT BE AVAILABLE IN ARBITRATION.
There shall be no right or authority for any Claims to be arbitrated on a class action basis or on any basis involving Claims brought in a purported representative capacity on behalf of the general public, other establishments which accept the Card (Service Establishments), or other persons or entities similarly situated. Furthermore, Claims brought by or against a Service Establishment may not be joined or consolidated in the *307 arbitration with Claims brought by or against any other Service Establishment(s), unless otherwise agreed to in writing by all parties.
Thus, the Card Acceptance Agreement not only precludes a merchant from bringing a class action lawsuit, it also precludes the signatory from having any claim arbitrated on anything other than an individual basis. The Card Acceptance Agreement further provides as follows:
This arbitration provision is made pursuant to a transaction involving interstate commerce, and shall be governed by the Federal Arbitration Act, 9 U.S.C. Sections 1-16, as it may be amended (the FAA). The arbitrator shall apply applicable substantive law consistent with the FAA.... In conducting the arbitration proceeding, the arbitrator shall not apply the Federal or any state rules of civil procedure or rules of evidence. The arbitrator shall apply the applicable provisions of the Code of Procedure of the NAF, JAMS or AAA, as applicable to matters relating to evidence and discovery.[5]
D. The Plaintiffs' Substantive Claims. The plaintiffs' dispute with Amex rests upon the distinction between "charge cards" and "credit cards." The district court explained the distinction as follows:
A charge card requires its holder to pay the full outstanding balance at the end of a standard billing cycle. A credit card, by contrast, allows the cardholder to pay a portion of the amount owing at the close of a billing cycle, subject to interest charges. In plain terms, the credit card is a means of financing purchases, the charge card is a method of payment.
In re American Express Merchants Litig., 2006 WL 662341, at *1 n. 6.
According to the plaintiffs, Amex had until recent years centered its business on the issuance of corporate and personal charge cards to corporate clients and affluent consumers. Amex is alleged to be the undisputed leader in this market, to the extent that it "issues Corporate Cards to at least 70% of the companies included in the Fortune 500, and is likewise the leading issuer of Corporate Cards to middle-market companies ... and small businesses." The plaintiffs further assert that "[h]olders of charge cards are more affluent than credit cardholders, and a vastly higher percentage of charge cards than credit cards are held by businesses and used for business travel and other corporate purposes." In fact, the plaintiffs allege that Amex itself contends that "the average purchase on an American Express card is 17% higher than the average purchase made on a credit card."
Thus, the holder of a charge card is likely to be "a higher class of customer" and, as such, is particularly attractive to merchants such as the plaintiffs. Amex is certainly not unaware of this attraction, and as a result of it, Amex has traditionally been able to charge high "merchant discount fees," which are the fees a card issuer withholds as a percentage of each *308 purchase made with its card at the merchant's establishment. These fees, the plaintiffs aver, "are at least 35% higher than competitive rates" applicable to mass-market credit cards such as Visa, Master-Card, and Discover.
Over the last decade, however, the plaintiffs contend that Amex's "business in the markets for credit card issuance and credit card services has grown dramatically." Specifically, Amex has in recent years created new credit card products "marketed to college students, young adults and others who would certainly not produce the high per-transaction spending that Amex uses to justify [the] high [merchant] discount fees. By leveraging its market power in corporate and personal charge cards, however, American Express was able to compel merchants to accept its new revolving credit card product[s] at the same elevated discount rate, which vastly exceeded the rate for comparable Visa, MasterCard or Discover products."
According to the plaintiffs, the vehicle of this compulsion is the "Honor All Cards" provision contained in the Card Acceptance Agreement. Under the Agreement, a merchant does not contract to accept any one Amex product as a form of payment. Rather, the Agreement applies
to your acceptance of American Express© Cards.... American Express Card(s) ... shall mean any card or other account access device issued by American Express Travel Related Services Company, Inc., or its subsidiaries or affiliates or its or their licensees bearing the American Express name or an American Express trademark, service mark or logo.
The plaintiffs assert that, by means of the "Honor All Cards" provision, merchants are faced with the choice of paying supracompetitive merchant discount fees (i.e., fees above competitive levels) on Amex's new mass-market products or "inevitably los[ing] a significant portion of the sales they receive from businesses, travelers, affluent consumers, and others" who are the traditional users of Amex charge cards. This, the plaintiffs claim, amounts to an illegal "tying arrangement," in violation of Section 1 of the Sherman Act, 15 U.S.C. § 1.[6]
E. The District Court's Decision. Amex moved to compel arbitration pursuant to the terms of the Card Acceptance Agreement. In its March 15, 2006 opinion, the district court granted Amex's motion, first holding that the arbitration clause in the Agreement was "a paradigmatically broad clause" which was certainly applicable to the dispute between the parties. In re American Express Merchants Litig., 2006 WL 662341, at *4. The district court proceeded to consider the plaintiffs' contention that enforcement of the class action waiver would effectively strip them of the ability to assert their claims because "each individual plaintiff would have to incur discovery costs amounting to hundreds of thousands of dollars, despite seeking average damages of only $5000." Id. The district court expressed skepticism that this argument amounted to much:

*309 Plaintiffs' contention ... that the costs of individual arbitration would eclipse the value of any potential recovery, ignores the statutory protections provided by the Clayton Act. Section 4 of the Clayton Act provides that "any person who shall be injured in his business or property by reason of anything forbidden in the anti-trust laws ... shall recover threefold the damages by him sustained, and the cost of suit, including a reasonable attorney's fee." 15 U.S.C. 15(a)....
Id. at *5 (footnote omitted).
This observation was quickly reduced to dicta, however. This is because the district court proceeded to hold that "[t]he enforceability of the collective action waivers is a claim for the arbitrator to resolve. Issues relating to the enforceability of the contract and its specific provisions are for the arbitrator, once arbitrability is established." Id. at *6. Thus, the district court concluded that all of the plaintiffs' substantive antitrust claims, as well the question of whether or not the class action waivers were enforceable, were subject to arbitration.
The plaintiffs also made two additional arguments before the district court. First, they contended that the class action waiver could not be enforced against those named plaintiffs who had contracted with Amex before the 1999 inclusion of the mandatory arbitration clause in the Card Acceptance Agreement. Amex purportedly informed these plaintiffs of the inclusion of the clause by means of an amendment to the Agreement. The plaintiffs contended, however, that (1) Amex had not produced sufficient evidence of the fact that the "pre-1999 plaintiffs" had ever received this amendment and (2) even if the plaintiffs had received the amendment, their original merchant contract with Amex did not allow the subsequent introduction of an arbitration clause. The district court rejected these arguments, concluding that the plaintiffs had not successfully rebutted the presumption of mailing to which Amex is entitled and that the arbitration amendment constituted a reasonable addition to the original merchant contract. Id. at *7-*9.
Second, the plaintiffs contended that the class action waiver was not enforceable against named plaintiffs and class members who were citizens of California because the waivers were unconscionable under that State's law. The district court concluded that this was "a substantive matter[ ] to be raised before the arbitrator." Id. at *9.
The district court concluded as follows: "[Amex's] motion to compel arbitration of all claims against it is granted. Since this Court finds that all of plaintiffs' claims against [Amex] are subject to arbitration, it further orders that plaintiffs' cases against [Amex] be dismissed." Id. at * 10. The plaintiffs filed a timely appeal.

ANALYSIS
Before we proceed to the weighing of the parties' arguments, we think it would be helpful to set forth some of the issues which are not raised on this appeal. Specifically, these are issues which are commonly raised in the general run of arbitration cases with which this Court is faced.
First, the plaintiffs are not contending that the mandatory arbitration clause contained in the Card Acceptance Agreement is not broad enough to cover their antitrust claims. See JLM Indus., Inc. v. Stolt-Nielsen SA, 387 F.3d 163, 175 (2d Cir.2004) (holding that antitrust claims were arbitrable under a broad arbitration clause even though the claims concerned "matters beyond the making of a particular contract between the parties and the *310 performance of its terms"). Further, while they certainly do not deny that this case is one of considerable legal and evidentiary complexity, the plaintiffs do not argue that their claims are too complex to be properly handled in arbitration. See id. at 181 (rejecting argument that claims involving a "horizontal price-fixing conspiracy" were beyond the capabilities of an arbitral panel). Nor do the plaintiffs take issue with the dicta in JLM to the effect that this Court would view "skeptically" any argument positing that the "assertion of class claims should serve as a bar or deterrent to sending" a case to arbitration. Id. at 180 n. 9. On the contrary, the plaintiffs expressly aver that they "are not averse to proceeding in a class-wide arbitration."[7] (Blue 29) The plaintiffs are therefore not seeking to revive "the ancient judicial hostility to arbitration" as a form of dispute resolution. Halligan v. Piper Jaffray, Inc., 148 F.3d 197, 200 (2d Cir.1998). In asking us to hold that the class action waiver in the Card Acceptance Agreement is unenforceable, however, the plaintiffs are implicitly asking us to limit the principle that "many features of arbitration by contract, including... procedure and choice of substantive law," Hall Street Assocs., LLC v. Mattel, Inc., ___ U.S. ___, 128 S.Ct. 1396, 1404, 170 L.Ed.2d 254 (2008), are to be left to the discretion of the contracting parties, unsupervised by judicial review.[8] Although we believe that it is a close question, we believe that the plaintiffs are correct.
A. Jurisdiction. Section 16(a)(3) of the FAA, 9 U.S.C. § 16(a)(3), provides that an appeal may be taken from "a final decision with respect to an arbitration that is subject to this title." Because "an order compelling arbitration and dismissing a party's underlying claims is a `final decision with respect to an arbitration,'" Green Tree Fin. Corp.-Alabama v. Randolph, 531 U.S. 79, 82, 121 S.Ct. 513, 148 L.Ed.2d 373 (2000), there is no dispute that this Court has jurisdiction to hear the instant appeal.
B. Who Should Decide Whether the Class Action Waiver is Enforceable? The plaintiffs argue  and we do not see that Amex posits any argument to the contrary  that the district court erred in holding that the question of the class action waiver's enforceability is a matter for *311 the arbitrator, not the court. This is plainly correct.
In Buckeye Check Cashing, Inc. v. Cardegna, the Supreme Court stated that
[c]hallenges to the validity of arbitration agreements ... can be divided into two types. One type challenges specifically the validity of the agreement to arbitrate. The other challenges the contract as a whole, either on a ground that directly affects the entire agreement (e.g. the agreement was fraudulently induced), or on the ground that the illegality of one of the contract's provisions renders the whole contract invalid.
546 U.S. 440, 444, 126 S.Ct. 1204, 163 L.Ed.2d 1038 (2006) (citation omitted). The Court then held that if there is a challenge to "`the arbitration clause itself  an issue which goes to the making of the agreement to arbitrate  the federal court may proceed to adjudicate it. But [the FAA] does not permit the federal court to consider claims [which challenge] the contract generally.'" Id. at 445, 126 S.Ct. 1204 (quoting Prima Paint Corp. v. Flood & Conklin Mfg. Co., 388 U.S. 395, 403-404, 87 S.Ct. 1801, 18 L.Ed.2d 1270 (1967)).
The plaintiffs are plainly challenging the Card Acceptance Agreement's arbitration clause insofar as they dispute the enforceability of its class action waiver and, by extension, the validity of the parties' agreement to arbitrate. Their "challenge is to the arbitration clause itself," id., rather than to the entirety of the Card Acceptance Agreement.[9] This appeal therefore involves "a gateway dispute about whether the parties are bound by a given arbitration clause," a dispute which "raises a question of arbritrability for a court to decide." Howsam v. Dean Witter Reynolds, Inc., 537 U.S. 79, 84, 123 S.Ct. 588, 154 L.Ed.2d 491 (2002) (internal quotation marks omitted); accord Kristian v. Comcast Corp., 446 F.3d 25, 55 (1st Cir.2006); Jenkins v. First Am. Cash Advance of Georgia, LLC, 400 F.3d 868, 877 (11th Cir.2005).[10] We will therefore proceed to consider whether the class action waiver contained in the Card Acceptance Agreement is enforceable.
C. The Enforceability of Class Action Waiver Provisions: General Considerations. The FAA was "enacted ... to replace judicial indisposition to arbitration," Hall Street, 128 S.Ct. at 1402, and is, as we acknowledged at the outset of this opinion, an expression of "a strong federal policy favoring arbitration as an alternative means of dispute resolution." Hartford Accident & Indem. Co. v. Swiss Reinsurance Am. Corp., 246 F.3d 219, 226 (2d Cir.2001). The favoring of arbitration is, however, somewhat tempered by the fact that "[a]rbitration is strictly a matter of contract." Thomson-CSF, S.A. v. Am. Arbitration Ass'n, 64 F.3d 773, 779 (2d Cir. 1995). Enhancing the federal policy favoring arbitration is therefore largely a matter of "mak[ing] arbitration agreements as *312 enforceable as other contracts, but not more so." Opals on Ice Lingerie v. Body-lines, Inc., 320 F.3d 362, 369 (2d Cir.2003) (internal quotation marks omitted).
This principle is set forth in Section 2 of the FAA, 9 U.S.C. § 2, which provides that an agreement to arbitrate "shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract." Section 2 is "the primary substantive provision" of the FAA which "create[s] a body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the" FAA. Moses H. Cone Memorial Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983). We join other Circuits that have evaluated arbitration clauses containing class action waivers under the federal substantive law of arbitrability. See Gay v. CreditInform, 511 F.3d 369, 394-95 (3d Cir.2007) (holding class action waiver to be enforceable under Section 2 of the FAA notwithstanding claim that waiver was unconscionable under state law); Kristian, 446 F.3d at 63 ("Although Plaintiffs' challenges to the enforceability of the arbitration agreements could be evaluated through the prism of state unconscionability law, we have chosen to apply a vindication of statutory rights analysis, which is also part of the body of federal substantive law of arbitration...."). We conclude that the plaintiffs here have demonstrated that enforcement of the class action waiver in the Card Acceptance Agreement to cover their claims against Amex under federal antitrust statutes would be incompatible with the federal substantive law of arbitration.
We begin by recognizing that insofar as a plaintiff may be said to possess a "right" to litigate an action in federal court as a class action under Rule 23 of the Federal Rules of Civil Procedure, the right "is a procedural right only, ancillary to the litigation of substantive claims." Deposit Guar. Nat'l Bank v. Roper, 445 U.S. 326, 332, 100 S.Ct. 1166, 63 L.Ed.2d 427 (1980). Nevertheless, the Supreme Court has repeatedly recognized the utility of the class action as a vehicle for vindicating statutory rights. This is especially true with respect to the Court's recognition that the class action device is the only economically rational alternative when a large group of individuals or entities has suffered an alleged wrong, but the damages due to any single individual or entity are too small to justify bringing an individual action. The Court made the point forcefully more than thirty years ago in the context of an antitrust action:
A critical fact in this litigation is that petitioner's individual stake in the damages award he seeks is only $70. No competent attorney would undertake this complex antitrust action to recover so inconsequential an amount. Economic reality dictates that petitioner's suit proceed as a class action or not at all.
Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 161, 94 S.Ct. 2140, 40 L.Ed.2d 732 (1974). Thus, as the Court later opined, "`[t]he policy at the very core of the class action mechanism is to overcome the problem that small recoveries do not provide the incentive for any individual to bring a solo action prosecuting his or her rights.'" Amchem Prods., Inc. v. Windsor, 521 U.S. 591, 617, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997) (quoting Mace v. Van Ru Credit Corp., 109 F.3d 338, 344 (7th Cir.1997)); see also Roper, 445 U.S. at 338, 100 S.Ct. 1166 ("[A class action] may motivate [plaintiffs] to bring cases that for economic reasons might not be brought otherwise[, thereby] vindicating the rights of individuals who otherwise might not consider it worth the candle to embark on litigation in which the optimum result might be more than consumed by the cost."); Shady *313 Grove Orthopedic Assocs., P.A. v. Allstate Ins. Co., 549 F.3d 137, 144 (2d Cir.2008) ("[C]lass actions are designed in large part to incentivize plaintiffs to sue when the economic benefit would otherwise be too small, particularly when taking into account the court costs and attorneys' fees typically incurred."); Carnegie v. Household Int'l, Inc., 376 F.3d 656, 661 (7th Cir.2004) ("[T]he realistic alternative to a class action is not 17 million individual suits, but zero individual suits, as only a lunatic or a fanatic sues for $30.00.").
The Supreme Court has at least implicitly held that a provision in an arbitration agreement barring class procedures is not per se unenforceable because, as noted above, it held in Bazzle that the question of whether or not an ambiguous arbitration clause contained a class action ban was a matter for the arbitrator, not the court, to decide. 539 U.S. at 453, 123 S.Ct. 2402. Beyond this oblique ruling, however, the Supreme Court has yet to squarely face the question of whether or not there are conditions under which a class action ban would be incompatible with the FAA. But, as both parties here acknowledge, the Court has decided cases which involved matters which, if ancillary, are certainly pertinent to this question.
Gilmer v. Interstate/Johnson Lane Corp., 500 U.S. 20, 111 S.Ct. 1647, 114 L.Ed.2d 26 (1991), involved a claim under the Age Discrimination in Employment Act ("ADEA"), 29 U.S.C. § 621 et seq. Specifically, the plaintiff, a manager at a brokerage firm, asserted that he had been terminated by the firm in violation of the ADEA. Id. at 23, 111 S.Ct. 1647. After the plaintiff had filed suit in federal district court, the defendant firm moved to compel arbitration pursuant to a mandatory arbitration provision contained in the rules of the New York Stock Exchange ("NYSE"), to which the plaintiff had agreed to be bound when he became a registered securities representative. Id. at 23-24, 111 S.Ct. 1647.
The Court held that because "[i]t is by now clear that statutory claims may be the subject of an arbitration agreement," the arbitration clause was enforceable "`unless Congress itself has evinced an intention to preclude a waiver of judicial remedies for the statutory rights at issue.'" Id. at 26, 111 S.Ct. 1647 (quoting Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 628, 105 S.Ct. 3346, 87 L.Ed.2d 444 (1985)). Even though the Court acknowledged that "the ADEA is designed not only to address individual grievances, but also to further important social policies," id. at 27, 111 S.Ct. 1647, the Court could discern no Congressional intent to preclude ADEA claims from being subject to arbitration. The Court also considered the plaintiff's argument to the effect "that arbitration procedures cannot adequately further the purposes of the ADEA because they do not provide for broad equitable relief and class actions." Id. at 32, 111 S.Ct. 1647. The Court rejected this contention:
As the court below noted, however, arbitrators do have the power to fashion equitable relief. Indeed, the NYSE rules applicable here do not restrict the types of relief an arbitrator may award, but merely refer to "damages and/or other relief." The NYSE rules also provide for collective proceedings. But even if the arbitration could not go forward as a class action or class relief could not be granted by the arbitrator, the fact that the ADEA provides for the possibility of bringing a collective action does not mean that individual attempts at conciliation were intended to be barred.
Id. (citations, internal quotation marks, and brackets omitted).
*314 Amex directs our attention to the final sentence of this passage, and other courts have relied upon it in upholding mandatory arbitration clauses. Amex Brief at 19. In particular, the Third Circuit, in Johnson v. West Suburban Bank, 225 F.3d 366 (3d Cir.2000), dealt with a claim under the Truth in Lending Act ("TILA"), 15 U.S.C. § 1601 et seq. The plaintiffs argued that their class action claim in federal court was not subject to mandatory arbitration because TILA
effectively create[s] an unwaivable right to bring a class action.... [In TILA,] Congress enacted a scheme in which the court hearing a class action could set a damage figure up to a certain amount for certain patterns of conduct. This judicial flexibility in imposing damages up to $500,000 only exists if a class action is allowed, as individual plaintiff claims are generally capped at $1,000. Therefore, a right of classes to a judicially crafted punitive remedy is lost if this court orders arbitration of Johnson's claims.
Id. at 377.
The Third Circuit held that "[t]his argument is unavailing in light of" Gilmer. Id. The court noted that Gilmer involved a claim under the ADEA, a statute which explicitly provides in its text for the bringing of class actions. Id. (citing 29 U.S.C. § 626(b)). In spite of this, the court concluded, "the Supreme Court still ruled that the ADEA did not preclude arbitration notwithstanding the unavailability of the class action remedy there." Id.; see also Carter v. Countrywide Credit Indus., Inc., 362 F.3d 294, 298 (5th Cir.2004) ("[W]e reject the [plaintiffs'] claim that their inability to proceed collectively [in arbitration] deprives them of substantive rights available under the [Fair Labor Standards Act.] The Supreme Court rejected similar arguments concerning the ADEA in Gilmer....").
We cannot agree with this view of Gilmer because a collective, and perhaps a class action remedy, in fact was available in that case. As set forth above, the Supreme Court explicitly noted that the arbitration rules of the NYSE provided for the conduct of collective arbitration. 500 U.S. at 32, 111 S.Ct. 1647. At the time Gilmer was decided, the NYSE's rules may also have permitted arbitration claims submitted as class actions. Compare NYSE Rule 600(d) (2008) ("A claim submitted as a class action shall not be eligible for arbitration under the Rules of the Exchange.") with NYSE Rule 600 (1991) (containing no prohibition on class actions). The statement in Gilmer that the arbitration clause would be enforceable "even if" class remedies were available evidences that the Court itself was uncertain, but acknowledged the probability, that class action were feasible under the NYSE's rules. Moreover, it is dicta that does not apply here. The plaintiffs do not proffer the argument rejected in Gilmer, namely that the class action waiver is unenforceable merely because the relevant statute allows class actions. Rather, the conundrum presented by the instant appeal is more nuanced: whether the mandatory class action waiver in the Card Acceptance Agreement is enforceable even if the plaintiffs are able to demonstrate that the practical effect of enforcement of the waiver would be to preclude their bringing Sherman Act claims against Amex in either an individual or collective capacity.
After the Third Circuit's decision in Johnson, the Supreme Court came somewhat closer to this issue in Green Tree Financial Corp.-Alabama v. Randolph. That case also involved a claim under TILA and a consideration of the enforcement of a mandatory arbitration clause. *315 The specific issue to be decided was "whether an arbitration agreement that does not mention arbitration costs and fees is unenforceable because it fails to affirmatively protect a party from potentially steep arbitration costs." Green Tree, 531 U.S. at 82, 121 S.Ct. 513. Specifically, the plaintiff argued "that the arbitration agreement's silence with respect to costs and fees creates a `risk' that she will be required to bear prohibitive arbitration costs if she pursues her claims in an arbitral forum, and thereby forces her to forgo any claims she may have had against [the defendants]." Id. at 90, 121 S.Ct. 513. The Court rejected this argument because the plaintiff had proved no more than that the asserted "risk" was hypothetical:
It may well be that the existence of large arbitration costs could preclude a litigant such as Randolph from effectively vindicating her federal statutory rights in the arbitral forum. But the record does not show that Randolph will bear such costs if she goes to arbitration. Indeed, it contains hardly any information on the matter.... The record reveals only the arbitration agreement's silence on the subject, and that fact alone is plainly insufficient to render it unenforceable. The "risk" that Randolph will be saddled with prohibitive costs is too speculative to justify the invalidation of an arbitration agreement.
Id. at 90-91, 121 S.Ct. 513 (footnote omitted); see also In re Cotton Yarn Antitrust Litigation, 505 F.3d 274, 285 (4th Cir.2007) ("[I]f a party could demonstrate that the prohibition on class actions likely would make arbitration prohibitively expensive, such a showing could invalidate an agreement.").
Although the Court in Randolph declined to consider whether the arbitration agreement was unenforceable because it may have precluded the plaintiff from bringing her claims under TILA as a class action, 531 F.3d at 92 n. 7, courts have relied upon its holding to uphold such bans. See In re Cotton Yarn Antitrust Litigation, 505 F.3d at 285 ("This kind of uninformed speculation about cost falls far short of satisfying the plaintiffs' burden of proving that the costs of proceeding individually against the defendants would be prohibitive and thus would prevent them from effectively vindicating their statutory rights."); Livingston v. Assocs. Fin., Inc., 339 F.3d 553, 557 (7th Cir.2003) ("In the present case, the Livingstons have not offered any specific evidence of arbitration costs that they may face in this litigation, prohibitive or otherwise, and have failed to provide any evidence of their inability to pay such costs...."); Adkins v. Labor Ready, Inc., 303 F.3d 496, 503 (4th Cir. 2002) ("Adkins makes no showing of the specific financial status of any of the plaintiffs at the time this action was brought. He provides no basis for a serious estimation of how much money is at stake for each individual plaintiff.").
D. Is the Class Action Waiver in the Card Acceptance Agreement Enforceable? Randolph is controlling here to the extent that it holds that when "a party seeks to invalidate an arbitration agreement on the ground that arbitration would be prohibitively expensive, that party bears the burden of showing the likelihood of incurring such costs." 531 U.S. at 92, 121 S.Ct. 513. We find that the district court erred in ruling that the plaintiffs had failed to bear this burden because they had "ignore[d] the statutory protections provided by the Clayton Act." In re American Express Merchants Litigation, 2006 WL 662341, at *5. On the contrary, the record abundantly supports the plaintiffs' argument that they would incur prohibitive costs if compelled to arbitrate under the *316 class action waiver.[11] The Card Acceptance Agreement therefore entails more than a speculative risk that enforcement of the ban will deprive them of substantive rights under the federal antitrust statutes.
This argument is compellingly set forth in an affidavit filed in the district court by Gary L. French, Ph.D., an economist associated with Nathan Associates Inc., a financial consulting firm retained by the plaintiffs. Dr. French states that the purpose of his affidavit is "to provide an expert opinion concerning the likely costs and complexity of an expert economic study concerning the liability and damages" relating to this action, and to compare this with "the potential recovery of damages by an American Express Card merchant with annual sales volume of $10 million or less, such as most if not all of the named plaintiffs in this litigation, and to provide my opinion as to whether it would be economically rational for such a merchant to pursue recovery of damages given the likely out-of-pocket costs of the arbitration or litigation proceeding." Dr. French continues:
Due to the complexity and analytical intensity of an antitrust study, total expert fees and expenses usually are substantial, even in a non-class action involving an individual plaintiff. In my experience, even a relatively small economic antitrust study will cost at least several hundred thousand dollars, while a larger study can easily exceed $1 million.... In summary, the cost of [Nathan Associates'] expert assistance in individual plaintiff antitrust cases has ranged from about $300 thousand to more than $2 million. However, after reviewing the complaint and doing some preliminary research in this case, it is my opinion that ... the cost for this case will fall in the middle of the range of [Nathan Associates'] experience.
An economic antitrust study ... is necessarily complex and costly because it involves investigating several antitrust liability and damages issues and, potentially involves numerous tasks and services. The antitrust liability and damages issues that an expert economist will study in this matter will likely include:
 defining the relevant tying and tied product markets and determining whether they are distinct;
 determining whether the defendant has market (monopoly) power in the tying product market, ...;
 determining whether the defendant has exercised its market (monopoly) power to enforce the tying arrangement;
 determining whether the tying arrangement has an anticompetitive effect in the tied product market;
 determining what the merchant fees would have been but for the alleged anticompetitive tying; and
 quantifying the dollar amount of damages to the plaintiffs as a consequence of the tying arrangement.
Dr. French then proceeds to consider the economic rationality of bringing an *317 individual action against Amex in light of these substantial expert witness costs:
Based upon publicly available information... I have estimated that a small merchant with $10 million of annual sales, on average, might calculate and expect $754 of economic damages for the year 2001, which is roughly the midpoint of the damage period covered by this litigation.... Multiplying the $754 damage figure by four, gives a rough estimate of $3,015 total damages for the whole four-year damage period, or $9,046 when trebled, assuming that the merchant's sales remain constant at $10 million for the four-year period.
... The median volume merchant, with half of the named plaintiffs having more and half having less American Express charge volume, and having reported $230,343 American Express Card volume in 2003, might expect four-year damages of $1,751, or $5,252 when trebled.... The largest volume named plaintiff merchant, with reported American Express Card volume of $1,690,749 in 2003, might expect four-year damages of $12,850, or $38,549 when trebled.
In my opinion as a professional economist... it would not be worthwhile for an individual plaintiff ... to pursue individual arbitration or litigation where the out-of-pocket costs, just for the expert economic study and services, would be at least several hundred thousand dollars, and might exceed $1 million.
In Kristian, the First Circuit found that expert affidavits similar to Dr. French's "demonstrat[ed] that without some form of class mechanism  be it class action or class arbitration  a consumer antitrust plaintiff will not sue at all." 446 F.3d at 58. We hold that the plaintiffs here have also demonstrated that their antitrust claims against Amex can, for all intents and purposes, only be pursued through the aggregation of individual claims, either in class action litigation or in class arbitration.
The district court, which held that the enforceability of the class action waiver in the Card Acceptance Agreement was a matter to be determined in arbitration, did not deal head on with Dr. French's affidavit. Dr. French's conclusion that "in a non-class action involving an individual plaintiff ... even a relatively small economic antitrust study will cost at least several hundred thousand dollars" was essentially uncontested. Instead of addressing this figure, the district court misinterpreted and misapplied the statutory protections available to the plaintiffs. Citing Section 4 of the Clayton Act, 15 U.S.C. § 15(a), the district court noted that a plaintiff who had established a Sherman Act claim against a defendant "shall recover threefold the damages by him sustained, and the cost of suit, including a reasonable attorney's fee." In re American Express Merchants Litig., 2006 WL 662341, at *5; see also Dambrosio v. Comcast Corp., No. Civ.A.03-6604, 2005 WL 3543794, at *16 (E.D.Pa. Dec.27, 2005) (asserting that Section 4 of the Clayton Act "expressly provides for the recovery of attorneys' fees and expenses, [thereby] making the arbitral forum accessible to individual plaintiffs and allowing them to vindicate the full range of substantive rights granted to them" under the federal antitrust laws), vacated on other grounds, 2006 WL 2058643 (E.D.Pa. Apr.12, 2006).
This is true, but, as the plaintiffs correctly point out, the Clayton Act simply does not solve their problem. Besides the fact that the trebling of a small individual damages award is not going to pay for the expert fees Dr. French has estimated will be necessary to make an individual plaintiff's case here, there is an even more *318 important legal consideration that the district court did not consider. In Crawford Fitting Co. v. J.T. Gibbons, Inc., the Supreme Court addressed fee-shifting for expert witnesses under Rule 54(d) of the Federal Rules of Civil Procedure in an antitrust case, holding that "when a prevailing party seeks reimbursement for fees paid to its own expert witnesses, a federal court is bound by the limit of [28 U.S.C.] § 1821(b)...." 482 U.S. 437, 439, 107 S.Ct. 2494 (1987).[12] We note that that figure is now set at a $40 per diem. Further, as the plaintiffs assert, there are no provisions "in the rules of any of the arbitral bodies designated [in the Card Acceptance Agreement] that would allow such costs to be awarded where they are not authorized by the applicable fee shifting statute." Even with respect to reasonable attorney's fees, which are shifted under Section 4 of the Clayton Act, the plaintiffs must include the risk of losing, and thereby not recovering any fees, in their evaluation of their suit's potential costs.[13] Thus, Amex's reply to the effect that "[a]n arbitrator can award the same reasonable costs that are recoverable by statute," plainly does not solve the problem.
Amex also informs us that a putative antitrust class action challenging the "Honor All Cards" provision in the Card Acceptance Agreement has been brought in the U.S. District Court for the Southern District of New York by a merchant plaintiff who is apparently not subject to the class action waiver provision in the Agreement. See The Marcus Corp. v. American Express Co., No. 04cv5432, 2005 WL 1560484 (S.D.N.Y. July 5, 2005). Further pointing out that the plaintiffs in that action are represented by the same counsel who represent the plaintiffs here, Amex speculates that "[p]resumably" the plaintiffs here, "the Marcus plaintiff, and their common attorneys and experts could reach an agreement as to how the experts' cost of preparation could be shared." This is an intriguing proposition, but we do not believe it can survive the application of the following provision of the arbitration clause in the Card Acceptance Agreement: "The arbitration proceeding and all testimony, filings, documents and any information relating to or presented during the arbitration proceedings shall be deemed to be confidential information not to be disclosed to any other party." Thus, any proposal that the plaintiffs share the services of expert witnesses employed in the Marcus action runs aground on the fact that the individual plaintiffs have contracted with Amex not to share such information with anyone.[14]
*319 Concluding that Amex has brought no serious challenge to the plaintiffs' demonstration that their claims cannot reasonably be pursued as individual actions, whether in federal court or in arbitration, we find ourselves in agreement with the plaintiffs' contention that enforcement of the class action waiver in the Card Acceptance Agreement "flatly ensures that no small merchant may challenge American Express's tying arrangements under the federal antitrust laws." The effective negation of a private suit under the antitrust laws is troubling because such "private suits provide a significant supplement to the limited resources available to the Department of Justice for enforcing the antitrust laws and deterring violations." Reiter v. Sonotone Corp., 442 U.S. 330, 344, 99 S.Ct. 2326, 60 L.Ed.2d 931 (1979). This may be especially true with respect to private antitrust suits brought as class actions. See Dando B. Cellini, "An Overview of Antitrust Class Actions," 49 Antitrust L.J. 1501, 1506 (1980) ("I think it is obvious from the experience over the last fifteen years since the 1966 amendments to Rule 23 were adopted that linking an antitrust claim with a class action allegation can be devastatingly effective.").
In Mitsubishi, the Supreme Court held that there is by no means any necessary reason to prevent sending a Sherman Act claim to arbitration because "so long as the prospective litigant effectively may vindicate its statutory cause of action in the arbitral forum, the statute will continue to serve both its remedial and deterrent function." 473 U.S. at 637, 105 S.Ct. 3346. The Mitsubishi Court recognized, however, that there might be instances in which an arbitration agreement contained provisions that would be unenforceable because they would prevent a prospective litigant from vindicating its rights under the Sherman Act in an arbitral forum. Specifically, the plaintiff in Mitsubishi speculated that the choice-of-forum and choice-of-law clauses in the arbitration agreement at issue would effectively preclude the arbitrator from determining the plaintiff's substantive claims in accordance with the terms of the Sherman Act. The Court responded that it would not prevent the case from going to arbitration based upon mere conjecture as to what body of law the arbitrator would apply, but also continued as follows:
We merely note that in the event the choice-of-forum and choice-of-law clauses operated in tandem as a prospective waiver of a party's right to pursue statutory remedies for antitrust violations, we would have little hesitation in condemning the agreement as against public policy.
Id. at 637 n. 19, 105 S.Ct. 3346.
We readily acknowledge that this statement is dicta, but it is nevertheless dicta grounded upon a firm principle of antitrust law to the effect that an agreement which in practice acts as a waiver of future liability under the federal antitrust statutes is void as a matter of public policy. More than a half-century ago, the Supreme Court stated that "in view of the public interest in vigilant enforcement of the antitrust laws through the instrumentality of the private treble-damage action," an agreement which confers even "a partial immunity from civil liability for future violations" of the antitrust laws is inconsistent with the public interest. Lawlor v. Nat'l Screen Serv. Corp., 349 U.S. 322, 329, 75 S.Ct. 865, 99 L.Ed. 1122 (1955); see also Minnesota Mining and Mfg. Co. v. Graham-Field, *320 Inc., No. 96cv3839, 1997 WL 166497, at *3 (S.D.N.Y. Apr.9, 1997) ("GFI could not have waived [its antitrust] claim in the releases because a prospective waiver of an antitrust claim violates public policy.").
We believe that one of the amici has correctly applied the principle just set forth to the facts of the instant case:
Plaintiff[s]-appellants' antitrust claims are complex and plaintiffs established for the record below that if they are precluded from participating in a collective action, the cost to each individual consumer to prosecute his or her claim is prohibitive relative to the consumer's potential recovery. If the collective action waiver is enforced, American Express will be shielded from liability, even where it may have violated the antitrust laws. Eradicating the private enforcement component from our antitrust law scheme cannot be what Congress intended when it included strong private enforcement mechanisms and incentives in the antitrust statutes. Because the class action waiver precluded the plaintiff[s]-appellants from enforcing their statutory rights, the arbitration provision is unenforceable.
Brief of American Antitrust Institute at 15; see also Dale v. Comcast Corp., 498 F.3d 1216, 1224 (11th Cir.2007) ("Corporations should not be permitted to use class action waivers as a means to exculpate themselves from liability for small value claims.").
We therefore hold that the class action waiver in the Card Acceptance Agreement cannot be enforced in this case because to do so would grant Amex de facto immunity from antitrust liability by removing the plaintiffs' only reasonably feasible means of recovery. As already set forth, Section 2 of the FAA, 9 U.S.C. § 2, provides that an agreement to arbitrate "shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract." Given that we believe that a valid ground exists for the revocation of the class action waiver, it cannot be enforced under the FAA.
E. Two Caveats. We emphasize two important limitations upon our holding. First, our decision in no way rests upon the status of the plaintiffs as "small" merchants. The plaintiffs repeatedly refer to themselves as "small merchants" and as "small businesses." But Amex is correct when it counters that the plaintiffs "undoubtedly hope that, by labeling themselves as `small,' they can benefit from one line of case law where individual consumers have alleged that arbitration agreements were imposed as a result of unequal bargaining power." See, e.g., Lowden v. T-Mobile USA, Inc., 512 F.3d 1213, 1219 (9th Cir.2008) (holding class action waiver contained in cellular telephone unconscionable under Washington law); Skirchak, 508 F.3d at 60 (holding class action waiver in employment agreement unconscionable under Massachusetts law); Shroyer v. New Cingular Wireless Servs., Inc., 498 F.3d 976, 984 (9th Cir.2007) (holding class action waiver in cellular phone contract unconscionable under California law). We do not follow these cases because they all rely on findings of unconscionability under state law, while we have relied here on a vindication of statutory rights analysis, which is part of the federal substantive law of arbitrability. Applying the latter, we have found that plaintiffs have demonstrated the necessity of some class mechanism in order to bring their claims against Amex. This demonstration is in no way dependant on the "size" of any or all of the merchant plaintiffs; it depends upon a showing that the size of the recovery received by any individual plaintiff will be too small to justify the expenditure of bringing an individual action.
*321 Second, we stress that we do not hold here that class action waivers in arbitration agreements are per se unenforceable. We also do not hold that they are per se unenforceable in the context of antitrust actions.[15] Rather, we hold that each case which presents a question of the enforceability of a class action waiver in an arbitration agreement must be considered on its own merits, governed with a healthy regard for the fact that the FAA "is a congressional declaration of a liberal federal policy favoring arbitration agreements." Moses H. Cone Memorial Hosp., 460 U.S. at 24, 103 S.Ct. 927. We believe that the Eleventh Circuit has posited something like the correct approach:
[T]he enforceability of a particular class action waiver in an arbitration agreement must be determined on a case-by-case basis, considering the totality of the facts and circumstances. Relevant circumstances may include, but are not limited to, the fairness of the provisions, the cost to an individual plaintiff of vindicating the claim when compared to the plaintiff's potential recovery, the ability to recover attorneys' fees and other costs and thus obtain legal representation to prosecute the underlying claim, the practical affect the waiver will have on a company's ability to engage in unchecked market behavior, and related public policy concerns.
Dale, 498 F.3d at 1224.
F. The Plaintiffs' Other Claims. Because we hold that the class action waiver in the Card Acceptance Agreement is unenforceable as to all plaintiffs under the federal substantive law of arbitration, the plaintiffs' contention that the waiver is not enforceable against named plaintiffs and class members who were citizens of California because the waivers are unconscionable under that State's law is moot. Similarly, the plaintiffs' appeal of the district court's holding that the class action waiver could be enforced against those named plaintiffs who had contracted with Amex before the 1999 inclusion of the mandatory arbitration clause in the Card Acceptance Agreement is also moot.
G. Relief. Because the plaintiffs have declared themselves amenable to proceeding to arbitration, we need not consider whether the class action waiver in the Card Acceptance Agreement is severable from the remainder of the arbitration provision contained therein. Further, in light of the fact that Amex declared at oral argument that it would reconsider its intention to proceed to arbitration should this Court not enforce the class action waiver, we remand to the district court to allow Amex the opportunity to withdraw its motion to compel arbitration.

CONCLUSION
The decision of the district court is REVERSED. We REMAND to the district court for further proceedings consistent with this opinion.
NOTES
[1]  We note that two district courts in our Circuit have found class action waivers in mandatory arbitration clauses to be enforceable. In Sherr v. Dell, Inc, No. 05cv10097, 2006 WL 2109436 (S.D.N.Y. July 27, 2006), a consumer brought a putative class action suit against Dell alleging that certain of the latter's products had a dangerous tendency to overheat. The plaintiff asserted claims under the statutory and common law of New York. Id. at *1. Dell moved to compel arbitration and for the enforcement of a class action waiver contained in its sales contract, the terms of which were not even available to the consumer before purchase short of his calling a special telephone number or visiting a Dell internet site. Id. The district court granted the motion to compel, holding that the "plaintiff is not entitled to a class action suit or class-wide arbitration to vindicate the rights of everyone else with a similar problem. The [Federal Arbitration Act's] primary purpose is not to create a right to sue as a class. Its main purpose is to ensure that private agreements to arbitrate are enforced according to their terms." Id. at *7 (quotation marks omitted). The case was decided according to the law of Texas, which, the district court found, had incorporated the Federal Arbitration Act as part of its substantive law. Id.

Dumanis v. Citibank (South Dakota), N.A., No. 07cv6070, 2007 WL 3253975 (W.D.N.Y. Nov.2, 2007), was an action involving credit card interest rates brought under the federal Truth in Lending Act, 15 U.S.C. § 1601 et seq., and the New York General Business Law. The contract at issue had a South Dakota choice of law clause, and the decision was based upon the law of that state, not the federal law of arbitration. Id. at *2-*3. The district court enforced the class action waiver contained in the contract's mandatory arbitration clause, both because the plaintiff could have "opt[ed] out" of the arbitration clause by not renewing his credit card and because the plaintiff had not been stripped of any substantive remedies; he merely could not pursue them "in the arguably more-favorable context of a class action." Id.
We note that in neither Sherr nor Dumanis does it appear that the plaintiff made a substantial demonstration  which we hold that the plaintiffs have made here  to the effect that an inability to pursue arbitration on a class basis would be tantamount to an inability to assert their claims at all.
[2]  Two commentators have suggested that this is particularly so in the credit card industry: "Credit card companies have shown themselves to be even less enthusiastic about classwide arbitration than about class action litigation. The `devil you know' phenomenon is compounded by the uncertainty of judicial review of class certification in arbitration and the concomitant fear of a `renegade arbitrator' certifying a class and exposing a company to massive liability." Samuel Issacharoff & Erin F. Delaney, "Credit Card Accountability," 73 U. Chi. L.Rev. 157, 179 (2006).
[3]  Interestingly, when it enacted the Class Action Fairness Act of 2005, Congress itself found both utility and danger in the use of the class action device. Compare Pub.L. No. 109-2, § 2(a)(1), 119 Stat. 4 (2005) ("Class action lawsuits are an important and valuable part of the legal system when they permit the fair and efficient resolution of legitimate claims of numerous parties by allowing the claims to be aggregated ....") with id. at § 2(a)(2) ("Over the past decade, there have been abuses of the class action device that have  (A) harmed class members with legitimate claims and defendants that have acted responsibly; (B) adversely affected interstate commerce; and (C) undermined public respect for our judicial system.").
[4]  Amex confirmed at oral argument that this $10 million figure relates to purchases made with Amex products, not to purchases made by credit cards generally.
[5]  The plaintiffs make no challenge to this preemption of the Federal Rules of Civil Procedure by the rules of the various arbitration firms listed in the Card Acceptance Agreement. We note, however, that some commentators have argued that plaintiffs are placed at a distinct disadvantage by class arbitration rules of these firms. See Daniel R. Higginbotham, "Buyer Beware: Why the Class Arbitration Waiver Clause Presents a Gloomy Future for Consumers," 58 Duke L.J. 103, 123 (2008) ("Regarding many important issues ... the rules [of arbitration firms] are either silent or diverge significantly from the Federal Rules of Civil Procedure, raising serious questions as to the ability of class arbitration to adequately resolve disputes.").
[6]  In a definition that has become classic, the Supreme Court has defined a tying arrangement as "an agreement by a party to sell one product but only on the condition that the buyer also purchases a different (or tied) product, or at least agrees that he will not purchase that product from any other supplier." Northern Pacific Ry. Co. v. United States, 356 U.S. 1, 5-6, 78 S.Ct. 514, 2 L.Ed.2d 545 (1958). A tying arrangement will violate Section 1 of the Sherman Act if "the seller has appreciable economic power in the tying product market and if the arrangement affects a substantial volume of commerce in the tied market." Eastman Kodak Co. v. Image Technical Servs., 504 U.S. 451, 462, 112 S.Ct. 2072, 119 L.Ed.2d 265 (1992) (internal quotation marks omitted).
[7]  It is apparent that "[c]lass arbitration is a swiftly growing phenomenon. In late 2003, the American Arbitration Association (`AAA') introduced procedures for class arbitrations.... As of September 27, 2007, the AAA was administering more than 190 class arbitrations, and from July 10, 2006 until September 27, 2007 alone, the number of AAA-administered class arbitrations increased by more than 50%." David S. Clancy & Matthew M.K. Stein, "An Uninvited Guest: Class Arbitration and the Federal Arbitration Act's Legislative History," 63 Bus. Law. 55, 56 (2007). Clancy and Stein go on to argue that when Congress passed the Federal Arbitration Act, in 1925, it specifically envisioned arbitration as "something inherently prompt, inexpensive, and streamlined," and "did not expect that arbitrators would adjudicate anything like the modern class action...." Id. at 61, 67. Although the argument that class proceedings in arbitration are incompatible with the Federal Arbitration Act is an intriguing one, we are presented with no such argument on this appeal.
[8]  The principle was limited by the Court itself in Hall Street which held that parties are not free to compose arbitration agreements which provide for a greater scope of federal court review of arbitral awards than that set forth in the Federal Arbitration Act ("FAA"), 9 U.S.C. § 1 et seq, because this would be at odds with the FAA's "substantiat[ion of] a national policy favoring arbitration with just the limited review needed to maintain arbitration's essential virtue of resolving disputes straightaway." 128 S.Ct. at 1405.
[9]  The plaintiffs' challenge to the enforceability of the class action waiver is distinct from any contention to the effect that Amex's alleged tying arrangement renders the entire Card Acceptance Agreement invalid. See Amex Brief at 49. The latter issue is not before us.
[10]  In Green Tree Financial Corp. v. Bazzle, 539 U.S. 444, 123 S.Ct. 2402, 156 L.Ed.2d 414 (2003), the Supreme Court was faced with an arbitration agreement which was ambiguous as to whether it permitted arbitration proceedings to be conducted on a class basis. The Court concluded that this was a matter of contract interpretation which "should be for the arbitrator, not the courts, to decide." Id. at 453, 123 S.Ct. 2402. Here, we do not face an issue of contract interpretation; the Card Acceptance Agreement is unambiguous in forbidding arbitration to proceed on a class basis.
[11]  "We review ... mixed questions of law and fact either de novo or under the clearly erroneous standard depending on whether the question is predominantly legal or factual." United States v. Selioutsky, 409 F.3d 114, 119 (2d Cir.2005) (internal citations omitted). The plaintiffs' estimated expert witness fees were essentially undisputed. We review de novo the district court's application of the Clayton Act to undisputed facts. See Village of Grand View v. Skinner, 947 F.2d 651, 656 (2d Cir.1991) ("Because the issues presented on this appeal involve the application of a statutory standard to undisputed facts, the appropriate standard of review is de novo."). We note, however, that our ruling would not be different under a clearly erroneous standard.
[12]  Quoting Paschall v. Kansas City Star Co., 695 F.2d 322, 338-39 (8th Cir.1982), Amex suggests that if an expert's findings prove "to be so `crucial' and `indispensable' that an arbitrator determines that the case absolutely could not have been pursued without them, the arbitrator might award such costs." Amex Brief at 28 We are skeptical, however, that an arbitrator might follow Paschall because it appears unlikely that its holding survives Crawford Fitting Co. See Gilbert v. City of Little Rock, Ark., 709 F.Supp. 856, 862 (E.D.Ark.1987) (holding that Paschall is inconsistent with the holding of Crawford Fitting to the effect that expert witness fees are to be determined solely in accordance with 28 U.S.C. § 1821(b)).
[13]  The plaintiffs' counsel has submitted a detailed affidavit which estimates that the cost of depositions and document management would exceed $300,000.
[14]  One of the amici makes the following suggestion: "Whatever costs the Merchant Plaintiffs might ultimately bear in procuring expert testimony in this case, those costs may be offset by the cost savings of conducting an arbitration proceeding, rather than an all-out federal trial." Brief of Business Roundtable at 16. But this misses the point. While it may be true that an individual arbitration brought by a plaintiff will likely cost less than a trial in federal district court, the fact remains that the plaintiffs have demonstrated to our satisfaction that neither an individual arbitration, nor an individual litigation would make any economic sense in light of the likelihood that expert fees far in excess of any likely individual recovery would need to be expended in either action.
[15]  We note that the Fourth Circuit, in In re Cotton Yarn Antitrust Litigation, has upheld the enforcement in an antitrust action of a collective action ban contained in a contract between commercial parties. The case presented a claim of antitrust conspiracy, and the court pointed out that a bar upon joining the two defendants, who were jointly and severally liable, did not preclude the arbitrability of the claim because "co-conspirators are not necessary parties; a plaintiff can prove the existence of a conspiracy in an action against just one of the members of the conspiracy." 505 F.3d at 284. The court also noted "[t]he absence of an evidentiary record on ... the actual cost of individual proceedings and ... about the ability of the corporate plaintiffs to bear those speculative costs." Id. at 285. Again, such a record exists in the instant case.
