
604 F.3d 732 (2010)
Lateif DICKERSON, individually and on behalf of a class of others similarly situated, Clyde Davison Jr., individually and on behalf of a class of others similarly situated, Jimmy Hogans, individually and on behalf of a class of others similarly situated, Plaintiffs-Appellants,
v.
Janet NAPOLITANO, in her official capacity as Secretary of the Department of Homeland Security, Chris Pappas, Thomas Mahoney, Karlene Torres, Raymond Brockmann, John Doe, 1-50, Jane Doe, 1-50, City of New York, Defendants-Appellees.[*]
Docket No. 09-2167-cv.
United States Court of Appeals, Second Circuit.
Argued: January 12, 2010.
Decided: May 14, 2010.
*736 Jason J. Rozger, (Bruce Menken, of counsel), Beranbaum Menken Ben-Asher & Bierman LLP, New York, NY, for Plaintiffs-Appellants.
Sarah E. Light, Assistant United States Attorney (Benjamin H. Torrance, Assistant United States Attorney, of counsel), Preet Bharara, United States Attorney for the Southern District of New York, New York, NY, for Defendants-Appellees Napolitano, Pappas, and Mahoney.
Ellen Ravitch, Assistant Corporation Counsel (Stephen J. McGrath, Jennifer Rossan, of counsel), Michael A. Cardozo, Corporation Counsel of the City of New York, New York City Law Department, New York, NY, for Defendants-Appellees City of New York, Torres, and Brockmann.
Before: JACOBS, Chief Judge, SACK and HALL, Circuit Judges.
SACK, Circuit Judge:
In this appeal, the plaintiffs challenge, on various grounds, "Operation Stinking Badges,"[1] a joint federal-city policing policy, and New York City Administrative Code § 14-107, a New York City statute[2] criminalizing, inter alia, the possession without authority of "any uniform, shield,[3] buttons, wreaths, numbers or other insignia or emblem in any way resembling that worn by members of the police force." (emphasis added). Each plaintiff was arrested pursuant to Operation Stinking Badges and either section 14-107 or a New York State statute that criminalizes possession of a fraudulent instrument, for attempting to enter a federal building in New York City with objects resembling police badges.
The plaintiffs appeal from an order and a judgment of the United States District Court for the Southern District of New *737 York (Robert L. Carter, Judge). The order dismissed the plaintiffs' putative class-action complaint against two defendants for improper service of process. The judgment granted summary judgment to the remaining defendants on the merits, rejecting the plaintiffs' contentions that the Operation Stinking Badges policy provides for unconstitutional searches in violation of the Fourth Amendment and that section 14-107 is unconstitutionally void for vagueness in violation of the Fourteenth Amendment.
Operation Stinking Badges, the policy pursuant to which the plaintiffs were arrested, was a joint policing initiative between the Federal Protective Service ("FPS")[4] and the City of New York. Its goal was to deter persons with objects resembling badges used by police officers from entering specified federal buildings where they might use the badges to gain unauthorized admittance to the offices of federal agencies and other entities. Pursuant to the policy, during the security screening conducted at the entrance to such facilities, if FPS officers thought an object in the possession of a person seeking entry to be in violation of the policy, the potential offender was referred to the New York City Police Department ("NYPD"), and was subject to possible arrest, incarceration, and prosecution.
Each of the plaintiffs entered the federal building at 26 Federal Plaza in New York City on a separate occasion in possession of a badge that was thought by the security personnel to resemble a New York City Police Department shield. There is no allegation or evidence that the plaintiffs ever attempted or planned to attempt to use these badges in an improper way.
The plaintiffs were arrested, jailed, and prosecuted pursuant to either of two statutes Plaintiff Lateif Dickerson under New York City Administrative Code § 14-107, and Plaintiffs Clyde Davison Jr. and Jimmy Hogans under New York Penal Law § 170.20, a New York State statute criminalizing possession of a forged instrument. All charges against each plaintiff were ultimately dismissed.[5]
The plaintiffs subsequently brought the instant putative class-action lawsuit pursuant to, inter alia, 42 U.S.C. § 1983, Bivens v. Six Unknown Named Agents of Federal Bureau of Narcotics, 403 U.S. 388, 91 S.Ct. 1999, 29 L.Ed.2d 619 (1971), and corresponding state laws, challenging the Operation Stinking Badges policy on Fourth Amendment grounds. Although it is nowhere explicitly stated in the complaint, the plaintiffs subsequently articulated to the district court a challenge to section 14-107 on both First Amendment overbreadth and Fourteenth Amendment void-for-vagueness grounds. The district court dismissed all of the plaintiffs' claims. The plaintiffs reassert their First, Fourth, *738 and Fourteenth Amendment claims on appeal.
The plaintiffs waived their First Amendment overbreadth challenge to section 14-107. The claim was not explicitly asserted, and is not supported by the facts alleged, in the complaint. And although the plaintiffs did mention a First Amendment claim in their briefing in opposition to the defendants' motion to dismiss in the district court, they did not raise it during oral argument on that motion. We therefore decline to consider it on appeal.
No Fourteenth Amendment void-for-vagueness challenge of section 14-107 is made explicitly in the complaint either. The claim was, however, fully briefed and argued before the district court and was a basis for the district court's decision. There is also at least a colorable argument that it is central to the plaintiffs' Fourth Amendment claim, which was indeed asserted in the complaint. This claim fails on the merits, however, because in the absence of a constitutionally-protected right implicated by the plaintiffs' challenge to the statute, the plaintiffs are limited to an as-applied challenge. The statute is constitutional as applied to each of them.
Finally, the plaintiffs' Fourth Amendment challenge to their arrests pursuant to Operation Stinking Badges fails because there was probable cause for the arrests.
Because we conclude that the statute under which Dickerson was arrested is constitutional as it was applied to him, there was probable cause for his arrest, defeating his false arrest claim. Even though the other plaintiffs were charged with violation of New York Penal Law § 170.20, the fact that they could permissibly have been arrested pursuant to New York City Administrative Code § 14-107 provides probable cause for their arrests, thereby defeating their false arrest claims too.
For these reasons, we affirm the grant of summary judgment by the district court. We also affirm the dismissal of the complaint with respect to defendant Mahoney for insufficient service of process. On appeal, Pappas abandons his argument that he was improperly servedeven though the complaint as to him was dismissed in the district court on that basis. We nonetheless affirm the dismissal of all claims against Pappas for the same reasons that we affirm the grant of summary judgment in favor of the other defendants.

BACKGROUND
In April and July, 2006, the plaintiffs were arrested for entering the federal government office building at 26 Federal Plaza in Manhattan with badges resembling shields used by police officers[6] secured in their belongings. The building houses, among other things, the main office of the FBI's New York Division, the Department of Homeland Security U.S. Citizenship and Immigration Services, the New York Regional Office of the Social Security Office of Disability Adjudication and Review, and a day care facility for children of federal employees. See Feb. 23, 2007 Decl. of Thomas Mahoney in Support of Mot. for Summ. J. at ¶ 5, Dickerson et al. v. Chertoff et al., No. 06 cv 7615 (S.D.N.Y. Mar. 9, 2007) (Dkt. No. 16) ("Mahoney Decl."). The defendants have never asserted that the plaintiffs ever attempted, or planned to attempt, to use these badges as a means of *739 impersonating officers or gaining entry into any area of the building.
The plaintiffs were arrested pursuant to a joint federal-city policing initiative between FPS Region 2 and the New York City Police Department, Operation Stinking Badges, the goal of which was to "interdict[] fraudulent documents, police parking placards, and law enforcement style badges that may be used to gain unauthorized access to federal facilities." Mahoney Decl. at ¶ 5. Pursuant to this policy, FPS officers and special agents are authorized to verify the authenticity of any badge that is or resembles a police shield and that is in the possession of an individual attempting to enter a federal building. Under the policy, any person not authorized to carry a police shield who enters a federal building in possession of an item that resembles such a shield is subject to detention or arrest pursuant to any applicable city, state, or federal statute.
Upon each plaintiff's entry into 26 Federal Plaza, security screeners identified a badge in his possession and then contacted FPS agents who, after concluding that the badge in question was an offending badge, referred the plaintiff to the New York City Police Department Police Impersonation and Integrity Unit. Each plaintiff was subsequently taken to the New York Police Department 5th Precinct and there placed under arrest by one of the defendant New York City police officers.
Davison and Hogans were charged with violation of New York Penal Law § 170.20, which prohibits criminal possession of a forged instrument. Dickerson was charged with a violation of section 14-107, which prohibits possession of items that resemble certain objects used by New York City law enforcement personnel. Each plaintiff spent at least twenty hours in jail as a result. Charges against each were subsequently dropped or dismissed.
Following their respective arrests and subsequent releases, the plaintiffs brought the instant putative class-action lawsuit under, inter alia, 42 U.S.C. § 1983, Bivens v. Six Unknown Named Agents of Federal Bureau of Narcotics, 403 U.S. 388, 91 S.Ct. 1999, 29 L.Ed.2d 619 (1971), and corresponding state law provisions, alleging that they were unconstitutionally arrested, incarcerated, and prosecuted. The suit was filed against then-Secretary of the Department of Homeland Security Michael Chertoff, FPS Special Agents, NYPD detectives, unknown law enforcement officers, and the City of New York. During the course of the litigation, the plaintiffs have proffered three principal bases for the unconstitutionality of their arrests, incarcerations, and prosecutions. First, the plaintiffs alleged in their complaint that Operation Stinking Badges violates the Fourth Amendment and state-law rights to be free from false arrest because it is not illegal to possess the badges at issue. Second, the plaintiffs have attempted to articulate a void-for-vagueness theory of the unconstitutionality of section 14-107, the statute pursuant to which Dickersonbut not Davison or Hoganswas arrested, under the Due Process Clause of the Fourteenth Amendment, premised on the statute's allegedly insufficient notice of what conduct it prohibits and the unfettered discretion the statute allegedly provides to law enforcement officers. Third, the plaintiffs assert a violation of the First Amendment that is based not on any allegation of expressive conduct by the plaintiffs, but on the potential overbreadth of section 14-107. The latter two claims are not explicitly made in the complaint.
On March 9, 2007, the federal defendants Chertoff, FPS Special Agent Pappas, and FPS Special Agent Mahoney filed a motion to dismiss or, in the alternative, a motion for summary judgment. *740 The district court dismissed the action as against Pappas and Mahoney pursuant to Federal Rule of Civil Procedure 12(b)(5) for insufficient service of process. The court denied the plaintiffs' application for discovery or additional time to serve defendant Mahoney. Janet Napolitano, successor to Michael Chertoff as Secretary of Homeland Security, was substituted for Chertoff as a defendant pursuant to Federal Rule of Civil Procedure 25(d). Napolitano and the City defendants then moved to dismiss or, in the alternative, for summary judgment.
After hearing oral argument, the district court granted defendant Napolitano and the City defendants' motion for summary judgment on the grounds that Operation Stinking Badges did not violate the Fourth Amendment and that section 14-107 was constitutional under the Fourteenth Amendment because it both provided sufficient notice to allow an ordinary person to understand what was prohibited under the law and did not allow for arbitrary or discriminatory enforcement by law enforcement authorities. The district court's decision nowhere mentioned the plaintiffs' theory of relief under the First Amendment, which was raised in the plaintiffs' opposition to the defendants' motion to dismiss, see Pls.' Mem. of Law in Opp. to Fed. Defs.' Mot. to Dismiss at 12-13, Dickerson et al. v. Chertoff et al., No. 06 cv 7615 (June 15, 2007) (Dkt. No. 25) ("Pls.' Opp. to Mot. to Dismiss"), but was not alleged in the complaint or discussed at oral argument before the district court.
The plaintiffs appeal.

DISCUSSION

I. Standard of Review
We review the district court's grant of summary judgment de novo. Town of Southold v. Town of E. Hampton, 477 F.3d 38, 46 (2d Cir.2007). A grant of summary judgment is appropriate where "there is no genuine issue as to any material fact and [] the movant is entitled to judgment as a matter of law." Fed.R.Civ.P. 56(c)(2). In reviewing a motion for summary judgment, we construe all evidence in the light most favorable to the nonmoving party, drawing all inferences and resolving all ambiguities in its favor. LaSalle Bank Nat'l Ass'n v. Nomura Asset Capital Corp., 424 F.3d 195, 205 (2d Cir.2005).
We review a dismissal under Rule 12(b)(5) based on insufficient service of process for abuse of discretion. Thompson v. Maldonado, 309 F.3d 107, 110 (2d Cir.2002) (per curiam).

II. Vagueness of New York City Administrative Code § 14-107
Under New York City Administrative Code § 14-107, it is a crime, inter alia, "to have, use, wear or display without specific authority from the commissioner any uniform, shield, buttons, wreaths, numbers or other insignia or emblem in any way resembling that worn by members of the police force." Id. Such conduct is punishable by a fine or imprisonment.[7] The plaintiffs argue that the phrase "in any way resembling" renders the statute impermissibly *741 vague under the Fourteenth Amendment.
As an initial matter, there is some doubt about the viability of this claim because it is not explicitly made in the complaint. Inasmuch as (1) the district court accepted briefing on the claim, (2) the district court expressly considered it in rendering its opinion, (3) the defendants have not argued waiver of the claim, and (4) the claim can be understood as implicit in the plaintiffs' Fourth Amendment challenge, we conclude that it was not waived. See, e.g., Fed.R.Civ.P. 15(b)(2) ("When an issue not raised by the pleadings is tried by the parties' express or implied consent, it must be treated in all respects as if raised in the pleadings."); Jund v. Town of Hempstead, 941 F.2d 1271, 1287 (2d Cir.1991) (allowing claims not raised in complaint but briefed and argued without objection at the summary judgment stage and trial to be heard on appeal). We nonetheless reject this claim on its merits.
The Due Process Clause of the Fourteenth Amendment requires that every criminal statute (1) "give the person of ordinary intelligence a reasonable opportunity to know what is prohibited," and (2) "provide explicit standards for those who apply [the statute]." Grayned v. City of Rockford, 408 U.S. 104, 108, 92 S.Ct. 2294, 33 L.Ed.2d 222 (1972); see also Kolender v. Lawson, 461 U.S. 352, 358, 103 S.Ct. 1855, 75 L.Ed.2d 903 (1983) (requiring that criminal statutes contain "minimal guidelines to govern law enforcement" (internal quotation marks omitted)). The plaintiffs contend that neither requirement is met in this case.
The plaintiffs attempt to challenge section 14-107 both facially and as applied. The defendants dispute the plaintiffs' standing to raise a facial challenge, but argue that the plaintiffs' claims fail in any event. As discussed below, we conclude that section 14-107 was constitutionally applied to the plaintiffs despite reservations about the constitutionality of the statute were it subject to a facial vagueness challenge. The central question presented by this appeal therefore is whether the plaintiffs are permitted to bring their void-for-vagueness challenge facially. We conclude that they are not.

A. Facial and As-Applied Vagueness Challenges
Facial challenges are generally disfavored. See, e.g., Wash. State Grange v. Wash. State Republican Party, 552 U.S. 442, 450, 128 S.Ct. 1184, 170 L.Ed.2d 151 (2008) (recognizing that courts should "[e]xercis[e] judicial restraint in a facial challenge"); Farrell v. Burke, 449 F.3d 470, 494 (2d Cir.2006) ("Federal courts as a general rule allow litigants to assert only their own legal rights and interests, and not the legal rights and interests of third parties."). There are several rationales for limiting such third-party, or jus tertii, standing. First, doing so "serves institutional interests by ensuring that the issues before the court are concrete and sharply presented." Thibodeau v. Portuondo, 486 F.3d 61, 71 (2d Cir.2007) (internal quotation marks omitted). Second, "[c]laims of facial invalidity often rest on speculation." Wash. State Grange, 552 U.S. at 450, 128 S.Ct. 1184. Third, facial challenges "run contrary to the fundamental principle of judicial restraint that courts should neither anticipate a question of constitutional law in advance of the necessity of deciding it nor formulate a rule of constitutional law broader than is required by the precise facts to which it is to be applied." Id. (internal quotation marks omitted). Fourth, "facial challenges threaten to short circuit the democratic process by preventing laws embodying the will of the people from being implemented in a manner *742 consistent with the Constitution." Id. at 451, 128 S.Ct. 1184.
Despite courts' baseline aversion to facial challenges, the limitations on third-party standing that restrict such challenges are prudential, not jurisdictional. Courts are therefore permitted to recognize such standing and allow facial challenges in some cases. They have done so from time to time, particularlyand perhaps onlywhen the claims are based on the assertion of a First Amendment right. See Farrell, 449 F.3d at 495 n. 11.[8] In such cases, the plaintiff is allowed to challenge a law that may be legitimately applied to his or her own expressive conduct if the law has the potential to infringe unconstitutionally on the expressive conduct of others. See, e.g., Forsyth County, Ga. v. Nationalist Movement, 505 U.S. 123, 129, 112 S.Ct. 2395, 120 L.Ed.2d 101 (1992) ("It is well established that in the area of freedom of expression an overbroad regulation may be subject to facial review and invalidation, even though its application in the case under consideration may be constitutionally unobjectionable.").
The rationale for permitting a facial challenge, in the rare case where one is permissible, is that the "very existence of some broadly written laws has the potential to chill the expressive activity of others not before the court." Id. The potential for such a deterrent effect outweighs the prudential considerations that ordinarily militate against third-party standing.
[T]o require that the harm of "chilling effect" actually be suffered by the plaintiff would destroy the whole purpose of the concept, which is to enable even those who have not been chilled to vindicate the First Amendment interests of those who have . . . [and to] permit[] a person, who has standing to challenge governmental action because of the concrete harm it causes him, to assert a deficiency which may not affect him but only others.
United Presbyterian Church in the U.S.A. v. Reagan, 738 F.2d 1375, 1379 (D.C.Cir. 1984).
In order to decide whether the plaintiffs in this case can mount a facial challenge, then, the threshold question is whether their claim properly can be understood as arising under the First Amendment.

B. The Plaintiffs' First Amendment Vagueness Challenge
The plaintiffs' claim could conceivably have been characterized as a First Amendment challenge. They chose not to do so in the complaint, however. There it is pleaded as a pure Fourth Amendment claim for false arrest and malicious prosecution. The complaint makes no mention of, or allusion to, the First Amendment or any conduct that would implicate the First Amendment. At no point do the plaintiffs allege an "intent [to use the badges] to convey a particularized message." Texas v. Johnson, 491 U.S. 397, 404, 109 S.Ct. 2533, 105 L.Ed.2d 342 (1989) (internal quotation marks omitted). Indeed, the plaintiffs have been adamant throughout the litigation that the badges at issue were secured on their persons and that the plaintiffs engaged in no expressive conduct. See, e.g., Appellants' Br. at 5 ("None of the Plaintiffs in any way attempted to display these badges. . . ."). Similarly, the plaintiffs chose not to invoke the First Amendment at oral argument before the district court. The district court's opinion *743 therefore understandably did not engage in any First Amendment analysis.
Any First Amendment claim was therefore waived. See, e.g., Singleton v. Wulff, 428 U.S. 106, 120, 96 S.Ct. 2868, 49 L.Ed.2d 826 (1976) ("It is the general rule, of course, that a federal appellate court does not consider an issue not passed upon below."); N.Y. City Envtl. Justice Alliance v. Giuliani, 214 F.3d 65, 67 n. 2 (2d Cir. 2000) ("Because plaintiffs' purported § 1983 claim was neither raised in the complaint nor passed upon by the district court, we decline to review it on this appeal.").[9]

C. The Plaintiffs' Non-First Amendment Vagueness Challenge
Whether a facial void-for-vagueness challenge can be maintained when, as here, a challenge is not properly based on the First Amendment is unsettled.[10]See Farrell, 449 F.3d at 495 n. 12 (recognizing that City of Chicago v. Morales, 527 U.S. 41, 119 S.Ct. 1849, 144 L.Ed.2d 67 (1999), cast doubt on previous cases that had limited facial challenges for vagueness, but declining to resolve the conflict between the two competing standards); United States v. Rybicki, 354 F.3d 124, 131-32 (2d Cir. 2003) (en banc) (same). There are two potential standards that may govern non-First Amendment vagueness challenges. As the plaintiffs would not be permitted to bring a facial challenge under either standard, we need not resolve which standard should apply here.
The first possible standard for evaluating facial challenges outside of the First Amendment context is that such challenges are permitted only when "no set of circumstances exists under which the [law] would be valid." United States v. Salerno, 481 U.S. 739, 745, 107 S.Ct. 2095, 95 L.Ed.2d 697 (1987); accord Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 497, 102 S.Ct. 1186, 71 L.Ed.2d 362 (1982) ("To succeed [in a vagueness challenge], the complainant must demonstrate that the law is impermissibly vague in all of its applications."). This standard effectively eliminates facial challenges outside of the First Amendment context that could not also be brought as an as-applied challenge, since any law that *744 is unconstitutional in every set of circumstances is also necessarily unconstitutional when applied to any plaintiff.[11]See Rybicki, 354 F.3d at 129-30 (listing Second Circuit panel opinions that have "held that when . . . the interpretation of a statute does not implicate First Amendment rights, it is assessed for vagueness only `as applied'");[12]United States v. Nadi, 996 F.2d 548, 550 (2d Cir.1993) ("[V]agueness challenges that do not involve the First Amendment must be examined in light of the specific facts of the case at hand and not with regard to the statute's facial validity."), cert. denied, 510 U.S. 933, 114 S.Ct. 347, 126 L.Ed.2d 311 (1993). If this standard were to apply, the plaintiffs could not succeed in a facial vagueness challenge that was not premised on the First Amendment, unless the statute were also unconstitutionally vague as applied.
The second potential standard comes from Morales, where the Supreme Court expressed some skepticism about the Salerno/Hoffman Estates standard and upheld a facial vagueness challenge to an anti-loitering statute with no First Amendment implications. See Morales, 527 U.S. at 55 n. 22, 119 S.Ct. 1849 (Stevens, J., plurality opinion). Morales does suggest that facial challenges are permissible outside of the First Amendment context, but that case only permitted such a challenge in the presence of a constitutionally-protected right. See Morales, 527 U.S. at 53, 119 S.Ct. 1849 (Stevens, J., plurality opinion) ("[T]he freedom to loiter for innocent purposes is part of the `liberty' protected by the Due Process Clause."); id. at 55, 119 S.Ct. 1849 (stating that vague criminal laws that lack a mens rea requirement and infringe on constitutionally-protected rights are "subject to facial attack"). We are aware of no court that has read Morales so broadly as to permit facial challenges where no constitutional right is implicated. Indeed, our own Circuit has interpreted Morales to permit a non-First Amendment vagueness challenge only after concluding that "the law is `permeated' with vagueness, and, perhaps, that it infringes on a constitutional right and has no mens rea requirement." Rybicki, 354 F.3d at 131 (citing Morales, 527 U.S. at 55, 119 S.Ct. 1849); see also Arriaga v. Mukasey, 521 F.3d 219, 223 (2d Cir.2008) ("Although we have suggested that some facial vagueness challenges may be brought where fundamental rights are implicated outside the First Amendment context, we need not pursue that issue because [the plaintiff] has not identified a fundamental right compromised by the [challenged statute].").
Even if Morales were the controlling standard, which we have no reason to decide here, the plaintiffs would still be barred from bringing a non-First Amendment vagueness challenge because their complaint does not implicate any non-First Amendment constitutional right. At its most specific, the right suggested by the plaintiffs' challenge to the statute in this *745 case may be articulated as the right to possessbut not to use for expressive or other constitutionally-protected purposes[13] a physical item that looks like a shield used on official business by New York City police officers. We can find no basis in governing authority or history to support the notion that such a right, if it exists, is specifically protected by the Constitution.
To be sure, courts have characterized the rights implicated by statutes in vagueness challenges broadly. See, e.g., Morales, 527 U.S. at 53-54, 119 S.Ct. 1849 (Stevens, J., plurality opinion) (conceiving of the right implicated by an anti-loitering statute as the constitutionally-protected right to freedom of movement). But even so, due process concerns about vagueness or means of enforcement aside, we are unaware of any constitutional right that is impinged upon by the prohibition of the possession of bogus badges.[14]
The plaintiffs are therefore limited to an as-applied vagueness challenge under the Fourteenth Amendment.[15]

D. Vagueness Challenge under the Fourteenth Amendment
To successfully make an as-applied vagueness challenge, the plaintiffs must show that section 14-107 either failed to provide them with notice that possession of their badges was prohibited or failed to limit sufficiently the discretion of the officers who arrested them under the statute. See Grayned, 408 U.S. at 108, 92 S.Ct. 2294. The plaintiffs make neither showing.

1. Plaintiffs' As-Applied Challenge For Lack of Notice.
"[A]ll vagueness challenges," including those made as applied, "require us to answer . . . whether the statute gives adequate notice." Farrell, 449 F.3d at 485. A plaintiff making an as-applied challenge must show that the statute in question provided insufficient notice that his or her behavior at issue was prohibited. See id. at 490. The standard is an objective one. See id. at 483. Courts ask "whether *746 the law presents an ordinary person with sufficient notice of or the opportunity to understand what conduct is prohibited or proscribed," Thibodeau, 486 F.3d at 67, not whether a particular plaintiff actually received a warning that alerted him or her to the danger of being held to account for the behavior in question.
We understand the plaintiffs to argue, interestingly, that even if the literal words of New York City Administrative Code § 14-107 clearly apply to their conduct, the fact that the literal meaning of the words would also criminalize conduct that cannot conceivably actually be criminal would give an ordinary person a reason to believe that the conduct at issue in this case was not criminal either.
Section 14-107, taken literally, unambiguously prohibits possession of the badges that the plaintiffs possessed. The statute criminalizes possession of "any uniform, shield, buttons, wreaths, numbers or other insignia or emblem in any way resembling that worn by members of the police force." N.Y.C. Admin. Code § 14-107 (emphasis added). A literal reading of these words clearly criminalizes possession of any badge that is like, but not identical to, a police badge. This, rather than settling the matter, complicates it.
True, under the literal meaning of the statute, the plaintiffs knew that they were violating it. But it is difficult to conclude that a reasonable person would think that the statute means what it says. A literal reading of its prohibition of the possession of items "in any way resembling" a police uniform, shield, or insignia would criminalize possession of items that are widely held and openly displayed. How many children dressing up as police officers while trick-or-treating, or playingironically"cops" in a game of "cops and robbers," would be subject to arrest and prosecution under the statute's literal proscription of possession of a badge resembling a police shield?
It is worth noting that the NYPD is itself involved in selling such items. It licenses for sale, for example, a sticker that contains a decal of the NYPD Shield, and a variety of T-shirts, hats, and other clothing that, applying the terms of the statute literally, would seem in some way to "resembl[e]" the uniform worn by NYPD officers. See NYPD Store, available at http://www.nypd.com/ (last visited 5/3/10). That the sale of such articles is facilitated by the NYPD lends credence to the proposition that an ordinary person might think that possession of some articles that are covered by the literal words of the statute is not in fact prohibited.
In Morales, Justice Stevens was persuaded by a similar argument. Joined by two other Justices, he would have held that an anti-loitering statute that prohibited standing in public with a gang member provided insufficient notice to a reasonable person of what was forbidden despite the fact that the literal meaning of the statute was clear; such a literal meaning would mandate an application far beyond what was plausibly intended. Morales, 527 U.S. at 57, 119 S.Ct. 1849 (Stevens, J., plurality opinion) ("Since the city cannot conceivably have meant to criminalize each instance a citizen stands in public with a gang member, the vagueness that dooms this ordinance is not the product of uncertainty about the normal meaning of `loitering,' but rather about what loitering is covered by the ordinance and what is not.").
Were the plaintiffs in a position to raise a facial challenge, they might for this reason succeed. But, as we have explained, they are not. In their as-applied challenge, they must show not that section 14-107 provides insufficient notice to some people as to items that are prohibited, but *747 that it provided insufficient notice to the plaintiffs as to the specific items that they were arrested for possessing. And neither the widespread availability of hats and T-shirts bearing the NYPD logo, nor the prevalence of toy badges, would be likely to confuse a reasonable person as to the illegality of an adult carrying a facsimile of a police shield in his belongings while entering a government building. Even if there is ambiguity as to the margins of what conduct is prohibited under the statute, we are of the view that an ordinary person would understand the statute to prohibit the possession of items that could be used by an adult to impersonate a police officer. We therefore conclude that despite the unfortunate breadth of the statute, it gives reasonable notice that possession of a badge that resembles a police shield in circumstances where it might be used in order to mislead is prohibited.
Nor are we persuaded by the argument that the plaintiffs' badges were so different from authentic police badges that notice regarding a prohibition of possession of badges resembling police badges would not apply to those badges possessed by the plaintiffs. Plaintiff Davison was carrying an authentic, but unauthorized, New York City Transit Authority badge that he had failed to return upon ceasing employment for the New York City Transit Authority. Plaintiffs Dickerson and Hogans were each in possession of badges resembling official police badges in all respects other than the text on the face of the badges. There is evidence in the record that each could have been mistaken for a real police badge. See July 16, 2007 Reply Decl. of Thomas Mahoney in Support of Mot. for Summ. J. at ¶ 2, Dickerson et al. v. Chertoff et al., No. 06 cv 7615 (S.D.N.Y. July 20, 2007) (Dkt. No. 30) ("Mahoney Reply Decl.").[16] We conclude that "an ordinary person with sufficient notice of or the opportunity to understand what conduct is prohibited or proscribed" would understand that an unauthorized New York City Transit Authority badge or a badge that had been altered to state "New Jersey Firearms Academy Chief" or "Security Agent," but was in all other respects very much like an NYPD badge, would impermissibly resemble an NYPD badge. See Thibodeau, 486 F.3d at 67.

2. Plaintiffs' As-Applied Challenge For Lack of Sufficient Limits on Discretion of Officers Who Enforce the Statute.
Even if a person of ordinary intelligence has notice of what a statute prohibits, the statute nonetheless may be unconstitutionally vague "if it authorizes or even encourages arbitrary and discriminatory enforcement." Hill v. Colorado, 530 U.S. 703, 732, 120 S.Ct. 2480, 147 L.Ed.2d 597 (2000). To survive a vagueness challenge, a statute must "`provide[] explicit standards for those who apply it.'" Farrell, 449 F.3d at 492 (quoting Nadi, 996 F.2d at 550); see also Kolender, 461 U.S. at 358, 103 S.Ct. 1855 (requiring that statutes contain "minimal guidelines to govern law enforcement" (internal quotation marks omitted)). But a law need not "achieve `meticulous specificity,' which would come at the cost of `flexibility and reasonable breadth.'" Betancourt v. Bloomberg, 448 F.3d 547, 552 (2d Cir.2006) (quoting Grayned, 408 U.S. at 110, 92 S.Ct. 2294).
*748 Moreover, a statute that provides what may be unconstitutionally "broad discretion" if subjected to a facial challenge may still be upheld as constitutional on an as-applied challenge if "the particular enforcement at issue [is] consistent with the `core concerns' underlying the [statute]" such that "the enforcement did not `represent an abuse of the discretion afforded'" under the statute. Farrell, 449 F.3d at 493 (quoting Perez v. Hoblock, 368 F.3d 166, 177 (2d Cir.2004)). Courts therefore look to see "if the statute's meaning has a clear core." Id. (citing Smith v. Goguen, 415 U.S. 566, 573, 577-78, 94 S.Ct. 1242, 39 L.Ed.2d 605 (1974)).
We thus are presented with two questions: (1) Whether the "statute as a general matter provides sufficiently clear standards to eliminate the risk of arbitrary enforcement," and, if not, (2) whether, "even in the absence of such standards, the conduct at issue falls within the core of the statute's prohibition." Farrell, 449 F.3d at 494. The plaintiffs extensively briefed the first question, but barely addressed the second.
The plaintiffs argue persuasively that section 14-107 provides no "objective, verifiable standard" by which a police officer is to determine if the object is prohibited by the statute. Appellants' Br. at 22. The law itself criminalizes possession of articles "in any way resembling" those worn by police officers. N.Y.C. Admin. Code § 14-107. As we have discussed, this cannot mean what it says. See section II(D)(1), supra. Inasmuch as there are no standards provided by the statute to determine which objects in some way "resembl[e]" shields worn by members of the police force so as to be covered by the statute, the plaintiffs' argument that the standards are insufficient seems compelling.[17]
But even if the plaintiffs are successful in demonstrating a lack of sufficient standards governing enforcement, they must also establish that the prohibition of their badges does not fall within the "core concerns" underlying section 14-107. This they have not done. One of the plain purposes of the statute is to prohibit persons from bringing into secure facilities unauthorized badges that may later be used to impersonate a police officer and gain further unimpeded access to restricted areas. It was this initial prohibited act that the plaintiffs were arrested for engaging in here.
*749 The defendants submitted in support of their motion for summary judgment substantial uncontested evidence that "replica" or "bogus" police shields, gold badges made to look like NYPD shields, and other phony police paraphernalia, have been used to commit crimes. They also offered unrebutted testimony that such materials "may be used to gain unauthorized access to federal facilities." Mahoney Decl. at ¶ 5.[18] Such misuse strikes us as a core concern not only of the Operation Stinking Badges policy, but also of section 14-107, which by its terms is designed to stop "any person not a member of the police force [from] represent[ing] himself or herself falsely as being such a member."[19]
Because the enforcement at issue is consistent with the "core concerns" underlying section 14-107, we conclude that the plaintiffs' as-applied vagueness challenge for lack of adequate standards for enforcement fails.

III. Overbreadth of New York City Administrative Code § 14-107
The plaintiffs also argue that they should be permitted to bring a facial challenge to the statute based on its overbreadth that is, because it punishes someone else's constitutionally-protected behavioras distinguished from its alleged vagueness. Overbreadth, like facial vagueness, is an exception to the prudential rule forbidding parties from asserting the rights of third parties. See Farrell, 449 F.3d at 495 & n. 10. In the overbreadth context, third-party standing is permitted because of the potential deterrent effect of regulations on speech; it allows "those who have not been chilled to vindicate the First Amendment interests of those who have." United Presbyterian Church, 738 F.2d at 1379.
We reject the plaintiffs' overbreadth challenge for the same reason that we reject their First Amendment vagueness challenge: It is not raised in the complaint. The plaintiffs have neither pleaded facts to support the conclusion of, nor shown, their "intent to convey a particularized message," the "presen[ce]" of which is necessary "to bring the First Amendment into play." Johnson, 491 U.S. at 404, 109 S.Ct. 2533 (internal quotation marks omitted). We therefore conclude that this overbreadth argument has been waived.[20]


*750 IV. Breadth of Entry Search
The plaintiffs challenge both New York City Administrative Code § 14-107, the statute under which Dickerson was arrested, incarcerated, and prosecuted, and Operation Stinking Badges, the joint federal-city policy pursuant to which all three plaintiffs were searched and arrested upon entry to the federal building at 26 Federal Plaza. Irrespective of the constitutionality of section 14-107,[21] the plaintiffs argue that Operation Stinking Badges is unconstitutional under the Fourth Amendment because it mandates an illegal "entry search" that is "an unconstitutional extension of the `special needs' doctrine." Appellants' Br. at 31.
There is little basis for, and no case law of which we are aware to support, the proposition that the police cannot conduct a limited search upon entry to a public building for the purpose of identifying fake badges, much less authority for the proposition that entry searches must be limited to searches for weapons.
"The Fourth Amendment requires that searches and seizures be reasonable. A search or seizure is ordinarily unreasonable in the absence of individualized suspicion of wrongdoing." City of Indianapolis v. Edmond, 531 U.S. 32, 37, 121 S.Ct. 447, 148 L.Ed.2d 333 (2000). However, there are "limited circumstances in which th[is] usual rule does not apply," including "certain regimes of suspicionless searches where the program was designed to serve special needs, beyond the normal need for law enforcement." Id. (internal quotation marks omitted).
To determine whether the "special needs" of the government permit a search that would otherwise be impermissible under the Fourth Amendment, courts first examine whether the search serves as its immediate purpose an objective distinct from the ordinary evidence-gathering associated with criminal investigations. MacWade v. Kelly, 460 F.3d 260, 268 (2d Cir.2006). We are not persuaded by the plaintiffs' attempt to characterize searches pursuant to the challenged policy as methods of ordinary evidence-gathering to identify bogus badges. See Appellants' Br. at 33 (arguing that "it is clear that this policy is designed not to prevent the introduction of weapons, but to perform evidence gathering for ordinary criminal investigations; in other words, an unconstitutional entry search"). The evidence presented to the district court establishes without contradiction that the searches at issue are a means of ensuring the safety of federal buildings because objects that resemble badges, even if not displayed, present a significant security risk in the event the bearer gains access to the building. See Mahoney Reply Decl. ¶ 2.
Having been persuaded that the search provided for by Operation Stinking Badges served as its immediate purpose the "special" function of physically protecting federal buildings, we must decide whether such an entry search was reasonable. MacWade, 460 F.3d at 269. To determine reasonableness, courts consider (1) the weight and immediacy of the government interest, (2) the nature of the privacy interest that is compromised by the search, (3) the character of the intrusion *751 imposed by the search, and (4) the efficacy of the search in advancing the government interest. Id. In this case, the government interest in protecting federal buildings is substantial; the search in question is minimally intrusive, involving little more than passage through a metal detector; and the search appears to have been, to some extent, effective in locating bogus badges.
The only factor that bears any weight in the plaintiffs' favor is their privacy interest in not being screened upon entering a government building. While we recognize that plaintiffs do maintain a privacy interest in not being screened upon entrance to a building, this interest has routinely been found to be reasonably overcome in comparable searches evaluated and upheld by this and other courts. See, e.g., MacWade, 460 F.3d at 275 (upholding searches at subway stations); Cassidy v. Chertoff, 471 F.3d 67, 85 (2d Cir.2006) (upholding Department of Homeland Security's practice of searching carry-on baggage and vehicles of randomly selected passengers on a ferry); Wilkinson v. Forst, 832 F.2d 1330, 1340-41 (2d Cir.1987) (upholding certain searches at mass rallies); United States v. Edwards, 498 F.2d 496, 500 (2d Cir.1974) (upholding searches at airports); McMorris v. Alioto, 567 F.2d 897, 901 (9th Cir. 1978) (upholding search upon entry to state courthouse); Downing v. Kunzig, 454 F.2d 1230, 1232-33 (6th Cir.1972) (upholding searches upon entry to a federal building).
We conclude that the searches in question here were reasonable, and accordingly we find such searches conducted under the auspices of Operation Stinking Badges to be permissible under the "special needs" exception to the Fourth Amendment.

V. False Arrest
The plaintiffs' claim for false arrest is based on an asserted lack of probable cause for the plaintiffs' arrests. Appellants' Br. at 34-36. Probable cause is a complete defense to any action for false arrest or malicious prosecution in New York. See Jaegly v. Couch, 439 F.3d 149, 152 (2d Cir.2006); Burns v. City of N.Y., 17 A.D.3d 305, 305, 791 N.Y.S.2d 851, 851 (2d Dep't 2005). "An officer has probable cause to arrest when he or she has knowledge or reasonably trustworthy information of facts and circumstances that are sufficient to warrant a person of reasonable caution in the belief that the person to be arrested has committed or is committing a crime." Jaegly, 439 F.3d at 152 (internal quotation marks omitted). When an arrest is not made pursuant to a judicial warrant, the defendant in a false arrest case bears the burden of proving probable cause as an affirmative defense. Broughton v. State, 37 N.Y.2d 451, 458, 335 N.E.2d 310, 315, 373 N.Y.S.2d 87, 95 (1975).
We have concluded that New York City Administrative Code § 14-107, pursuant to which Dickerson was arrested, is constitutional as applied to him. See section II(A)-(D), supra. At least two sets of facts demonstrate that Dickerson's arrest comported with the terms of section 14-107, which criminalizes possession without authority of objects "in any way resembling" police badges: (1) the badge he was carrying resembled a police shield in shape, size, color, and design, and (2) Dickerson did not have specific official authority to possess it. The alterations of the badge in question do not change our view. An altered badge, which still "resembl[es]" an NYPD badge, may, if "flashed," mislead the person seeing it into thinking that it is legitimate. See Mahoney Reply Decl. ¶ 2. There was probable cause to arrest Dickerson, and his false arrest claim necessarily fails.
*752 Davison and Hogans were charged with violations of New York Penal Law § 170.20, a statute that makes it a crime for a person knowingly to possess a forged instrument with intent to defraud,[22] and not New York City Administrative Code § 14-107. Even assuming, as the plaintiffs contend, that either the forged instrument requirement or the intent requirement of New York Penal Law § 170.20 was not satisfied,[23] such a claim avails them nothing here because there was probable cause to arrest them under other statutes, such as New York City Administrative Code § 14-107 and, at least for plaintiff Hogans, New York General Business Law § 80.[24] Probable cause for arrest under these statutes is fatal to the plaintiffs' claim, because probable cause is based on the facts warranting arrest and not the statute pursuant to which a plaintiff was charged. See Devenpeck v. Alford, 543 U.S. 146, 153, 125 S.Ct. 588, 160 L.Ed.2d 537 (2004) (finding that the "subjective reason for making the arrest need not be the criminal offense as to which the known facts provide probable cause"); Jaegly, 439 F.3d at 153 ("The [Supreme] Court [has] rejected the view that probable cause to arrest must be predicated upon the offense invoked by the arresting officer, or even upon an offense `closely related' to the offense invoked by the arresting officer. . . ."). That the actual charges were brought under a different statute does not defeat a finding of probable cause. Id.[25]

VI. Injunctive Relief
Because we conclude that the search conducted pursuant to Operation Stinking Badges was a constitutional entry search and that New York Administrative Code § 14-107 is constitutional as applied to the plaintiffs in this case, the district court was correct to deny the plaintiffs' request for injunctive relief.

VII. Improper Service and Denial of Jurisdictional Discovery
"[W]hen a defendant moves to dismiss under Rule 12(b)(5), the plaintiff bears the burden of proving adequate service." Burda Media, Inc. v. Viertel, 417 F.3d 292, 298 (2d Cir.2005) (parentheses omitted). The plaintiffs stipulate that service on defendant Mahoney was inadequate, but argue that they should have *753 been provided discovery and additional time to effect service. We conclude that because the plaintiffs made neither a reasonable effort to effect service nor filed a motion for an extension of time to do so pursuant to Federal Rule of Civil Procedure 6(b), the district court did not abuse its discretion when it denied discovery or additional time.
With respect to defendant Pappas, the argument that service on him was improper has been abandoned on appeal. Assuming as we must that service on Pappas was proper, the dismissal of the case against him nonetheless was warranted for the same reasons that we affirm the grant of summary judgment in favor of the other defendants. See Alli-Balogun v. United States, 281 F.3d 362, 364 (2d Cir.2002) (affirming on grounds other than those relied on by the district court).

CONCLUSION
For the foregoing reasons, the order and judgment of the district court are affirmed.
NOTES
[*]  The Clerk is directed to amend the official caption accordingly.
[1]  The name was derived from familiar lines from the motion picture The Treasure of the Sierra Madre (Warner Bros.1948): "Badges? We ain't got no badges. We don't need no badges! I don't have to show you any stinkin' badges!" See Appellants' Br. at 10; http:// www.youtube.com/watch?v=VqomZQMZQCQ (last visited 5/3/10).
[2]  New York courts refer to provisions of the New York City Administrative Code as either "statutes" or "ordinances." Compare, e.g., In re Verizon N.Y., Inc. v. Envtl. Control Bd. of the City of N.Y., 68 A.D.3d 657, 657, 892 N.Y.S.2d 84, 85 (1st Dep't 2009) (employing "statute") with In re Cris Place, Inc. v. N.Y. State Liquor Auth., 56 A.D.3d 339, 339, 868 N.Y.S.2d 33, 34 (1st Dep't 2008) (employing "ordinance"). For ease of reference herein, section 14-107 is referred to as a statute.
[3]  We find no significance in the statute's use of the word "shield" and the frequent reference to police shields and items like them as "badges." We use the terms interchangeably.
[4]  FPS is an agency within the United States Immigration and Customs Enforcement, Department of Homeland Security, that is responsible for protecting the "buildings, grounds, and property that are owned, occupied, or secured by the Federal Government. . . and the persons on the property." 40 U.S.C. § 1315(a).
[5]  It is not clear from the record on appeal whether the charges against Dickerson and Davison were dismissed by the court or dropped by the prosecution. The charges against Hogans were dismissed by a New York Criminal Court judge. People v. Hogans, 2006 N.Y. 047746, Decision and Order at 3 (N.Y.Crim.Ct. Jan. 11, 2007) ("Mere possession of a facsimile badge, which does not falsely purport to be, on its face, the shield of an identifiable agency, cannot be the basis for a charge of criminal possession of a forged instrument [under N.Y. Penal Law § 170.20]." (internal quotation marks omitted)).
[6]  Dickerson's badge contained the words "New Jersey Firearms Academy Chief," but was similar in all other respects to a police badge; Davison's was an authentic New York City Transit Authority badge that he was no longer authorized to carry; and Hogans' contained the words "Security Agent," but was similar in all other respects to a police badge.
[7]  Section 14-107 provides in full:

It shall be unlawful for any person not a member of the police force to represent himself or herself falsely as being such a member with a fraudulent design upon persons or property, or to have, use, wear or display without specific authority from the commissioner any uniform, shield, buttons, wreaths, numbers or other insignia or emblem in any way resembling that worn by members of the police force. A violation of this section shall constitute a misdemeanor punishable by a fine of not more than one hundred dollars or by imprisonment for not more than sixty days, or both.
[8]  The rare situation where facial challenges have been permitted is discussed below. See section II(C), infra (discussing City of Chicago v. Morales, 527 U.S. 41, 119 S.Ct. 1849, 144 L.Ed.2d 67 (1999)).
[9]  The plaintiffs did attempt to argue in the alternative to the district court that despite the fact that they were not attempting to use the badges when they were arrested, there is an expressive purpose simply to possessing the badge; for example, Dickerson could use his New Jersey Firearms Academy Chief badge to proclaim his ownership of his business. See Pls.' Opp. to Mot. to Dismiss at 12-13. They repeat that argument here. Even if preserved, the argument fails to support the plaintiffs' vagueness claim. Appellants' Br. at 25. The plaintiffs explicitly argue that this argument is made "[s]eparately [from], and in the [a]ternative" to their vagueness argument. Appellants' Br. at 24. They thus eschew the notion that the vagueness claim, raised under the Fourteenth Amendment, is linked to the First Amendment challenge. We therefore decline to permit the plaintiffs to mount a facial vagueness challenge based upon the assertion of a First Amendment right.
[10]  The defendants contend that "[v]agueness challenges to statutes that do not implicate First Amendment rights are evaluated `as applied,' in light of the specific facts of the case at hand." City Appellees' Br. at 13. The plaintiffs concede that some cases have suggested this approach, but argue that cases such as Morales, 527 U.S. 41, 119 S.Ct. 1849, suggest that facial challenges to statutes are permissible whether or not the statutes implicate First Amendment rights. Appellants' Br. at 16-18. Inasmuch as there is confusion in the law, the plaintiffs ask this Court to "[r]enounce" past cases like United States v. Nadi, 996 F.2d 548, 550 (2d Cir.), cert. denied, 510 U.S. 933, 114 S.Ct. 347, 126 L.Ed.2d 311 (1993), holding that if a statute does not implicate the First Amendment, a vagueness challenge can only be brought as applied. Appellants' Br. at 17.
[11]  One potential case where an as-applied challenge may not be permitted under this standard but a facial challenge still conceivably could be permissible would be a challenge to a law that had not yet been, but potentially could be, applied unconstitutionally to the party challenging it. See, e.g., Laird v. Tatum, 408 U.S. 1, 11-13, 92 S.Ct. 2318, 33 L.Ed.2d 154 (1972) (discussing cases where facial challenges had been permitted based on, inter alia, the fact that the party challenging the law or regulation was "prospectively subject" to that law or regulation).
[12]  The Rybicki court itself expressed doubt about whether Supreme Court precedent eliminated facial challenges outside of the First Amendment context, and therefore declined to endorse the holding of this line of cases. See Rybicki, 354 F.3d at 131-32.
[13]  As noted above, we reject the plaintiffs' contention on appeal that the right implicated by their challenge is a First Amendment right to express ownership in a business because this argument is entirely absent from the complaint, because it contradicts their repeated claims that they were not attempting to use the badges for any expressive purpose, and because the argument regarding ownership is explicitly made "[s]eparately, and in the [a]lternative" to the plaintiffs' vagueness argument, which is to say that this argument is not implicated at all in the vagueness challenge. See section II(B), supra; Appellants' Br. at 24.
[14]  It may be that what the plaintiffs complain of is some sort of invasion of their privacy. If so, however, we do not understand what privacy right may be infringed by a person's inability to carry an ersatz badge. It is the responsibility of the party seeking to make a facial vagueness challenge to assert such a right; and failure to do so amounts to waiver of the issue. See Arriaga, 521 F.3d at 223 (declining to consider facial vagueness challenge where alien had not identified a constitutionally-protected right compromised by the immigration statute at issue in any of the prior proceedings). At no point in any of the prior proceedings have the plaintiffs articulated any constitutional privacy right infringed by the statute.
[15]  We reject the notion that the plaintiffs can assert a facial challenge based on the constitutionally-protected right to be free from an improper arrest. It is often the case that a constitutional challenge to an arrest implicates the right to be free from that arrest. If the infringement of such a right gave rise to a facial challenge, facial vagueness challenges would be the rule, not the exception. The constitutionally-protected right that must be implicated to support a facial challenge must be the right infringed by the statute that was applied to the plaintiffs, not the right infringed by the arrest for a violation of that statute.
[16]  Plaintiff Hogans, whose badge stated "Security Agent," was a licensed security guard who, through his licensing procedure, might well have been aware of New York General Business Law § 80, which restricts the badges worn by private security guards to "rectangular metal or woven insignia[s]."
[17]  The defendants argue that the statute explicitly sets out the items (e.g., shields) and the conduct (e.g., possession and use) that are prohibited. In support of this argument, both the city and federal defendants rely heavily on United States v. Goeltz, 513 F.2d 193 (10th Cir. 1975), in which the Tenth Circuit upheld 18 U.S.C. § 701, which prohibited the possession of any badge, identification card, or other insignia that was a replica of those prescribed by the head of any department, "or any colorable imitation thereof." Goeltz, 513 F.2d at 196 (quoting 18 U.S.C. § 701).

But the plaintiffs here are not challenging a prohibition of the possession of actual badges or colorable imitations thereof, but the prohibition of possessing objects "in any way resembling" badges. The "colorable imitation" standard that was present in Goeltz is far more specific than the "in any way resembling" standard that is present here. To illustrate: Plaintiff Dickerson altered his badge so that it stated in large letters "New Jersey Firearms Academy Chief," but in all other respects seems to be identical to an NYPD badge. The fact that the badge clearly stated it was not an NYPD badge would seem to remove it from the reach of 18 U.S.C. § 701, but the fact that it was so similar in other respects to an NYPD badge would seem to keep it within the "in any way resembling" language of section 14-107.
By using the language "in any way resembling," section 14-107 captures a whole host of conduct beyond that covered by 18 U.S.C. § 701, and provides no guidance for officers to determine what conduct is prohibited.
[18]  There is a risk that, once a person possessing such a fraudulent or unauthorized badge or other law enforcement paraphernalia enters 26 Federal Plaza and passes through the initial security screening, such an individual could use these items to gain unauthorized access to areas of 26 Federal Plaza reserved for authorized law enforcement personnel. Because [the building] houses both federal law enforcement agencies (including FPS, the FBI, and other law enforcement agencies), and non-law enforcement agencies, such as offices of the Social Security Administration and a Fed Kids day care facility, it is possible that non-law enforcement employees, who have no training in distinguishing between genuine and fraudulent law enforcement badges, would assume that an individual possessing a badge within the building is legally authorized to do so.

Mahoney Decl. at ¶ 5.
[19]  Two plaintiffs had slightly altered their badges, but there is no evidentiary basis for a conclusion that the badges could not be used to impersonate a police officer. See Mahoney Reply Decl. ¶ 2.
[20]  We nonetheless note that the Supreme Court has said, "[b]ecause of the wide-reaching effects of striking down a statute on its face at the request of one whose own conduct may be punished despite the First Amendment, we have recognized that the overbreadth doctrine is strong medicine and have employed it with hesitation, and then only as a last resort." Los Angeles Police Dep't v. United Reporting Publ'g Corp., 528 U.S. 32, 39, 120 S.Ct. 483, 145 L.Ed.2d 451 (1999) (internal quotation marks omitted). Unlike the vagueness doctrine, the overbreadth doctrine has unambiguously been restricted to First Amendment cases. See, e.g., United States v. Williams, 553 U.S. 285, 292, 128 S.Ct. 1830, 170 L.Ed.2d 650 (2008) ("According to our First Amendment overbreadth doctrine, a statute is facially invalid if it prohibits a substantial amount of protected speech."); Morales, 527 U.S. at 52-53, 119 S.Ct. 1849 (Stevens, J., plurality opinion).
[21]  Only one of the plaintiffs was charged with a violation of section 14-107. The other two plaintiffs were charged with a violation of New York Penal Law § 170.20, which prohibits possession of a forged instrument.
[22]  New York Penal Law § 170.20 provides, in full:

A person is guilty of criminal possession of a forged instrument in the third degree when, with knowledge that it is forged and with intent to defraud, deceive or injure another, he utters or possesses a forged instrument. Criminal possession of a forged instrument in the third degree is a class A misdemeanor.
[23]  The charges against Hogans were dismissed in New York City Criminal Court on the grounds that "[m]ere possession of a facsimile badge, which does not falsely purport to be, on its face, the shield of an identifiable agency, cannot be the basis for a charge of criminal possession of a forged instrument." People v. Hogans, 2006 N.Y. 047746, Decision and Order at 3 (N.Y.Crim.Ct. Jan. 11, 2007) (internal quotation marks omitted). We have no occasion to reconsider that conclusion on this appeal.
[24]  New York General Business Law § 80 is a statute that applies to licensed private investigators, bail enforcement agents, and watch, guard, and patrol agencies. Hogans was arrested for possession of a badge that stated "Security Agent," so could potentially be governed by this statute.
[25]  Even were the defendants not entitled to summary judgment on the merits of the false arrest claim because there was no probable cause to arrest under section 14-107, the individual police and FPS-officer defendants might well be entitled to qualified immunity based upon their reliance on the policy set out by Operation Stinking Badges. It is a question, though, that we need not and therefore do not reach.
