GIBBONS, J., delivered the opinion of the court, in which KEITH and GUY, JJ., joined. KEITH, J. (pp. 624-26), delivered a separate concurring opinion.
OPINION
JULIA SMITH GIBBONS, Circuit Judge.
Plaintiffs-appellants Johnny Robertson, Nolan Lovett, Arrico Spires, Charles Matthews, Marlon Brooks, and Tyron Brown appeal the district court’s grant of summary judgment to defendants-appellees Lee Lucas, Robert Cross, Thomas Verhi-ley, Jamaal Ansari, Chuck Metcalf, Matt Mayer, and Larry Faith, and the district court’s dismissal of appellants’ claims against Richland County and the City of Cleveland. Appellants argue that the district court erred in holding that the individual appellees were shielded by qualified immunity on their 42 U.S.C. § 1983 and Bivens claims; that judicial estoppel barred appellants’ false arrest claims; that because the individual appellees had not committed constitutional violations, appellants could not prevail on their Monell claims; and that appellants were not entitled to additional discovery. For the reasons stated below, we affirm.
I.
A.
This is yet another case in a series of civil rights cases arising out of a corrupted investigation into the Mansfield, Ohio, drug trade (the “Mansfield Investigation” or “Operation Turnaround”). As part of the investigation, the Richland County Sheriffs Office (“RCSO”) used a confidential informant it had used once before named Jerrell Bray. Bray’s primary task was to make controlled buys of illegal drugs from individuals in Richland County suspected of being involved in illegal drug activity.
In August or September 2005, the United States Drug Enforcement Agency (“DEA”) joined the Mansfield Investigation at the request of RCSO. Bray was registered as a DEA informant by Special Agents Robert Cross and Lee Lucas. Pri- or to DEA’s involvement, Bray made numerous buys for RCSO. Bray’s first buy as a DEA informant occurred on September 6, 2005.
Throughout the investigation, Bray was controlled principally by Detective Chuck Metcalf, Sergeant Matthew Mayer, and Captain Larry Faith of RCSO. Jamaal An-sari was a police officer with the City of [611]*611Cleveland Police Department detailed to the DEA’s Cleveland office and deputized as a DEA Task Force Officer pursuant to 21 U.S.C. § 878 during part of the Mansfield Investigation. Thomas Verhiley was a Special Agent with the Ohio Bureau of Criminal Identification and Investigation also detailed to the DEA’s Cleveland office and deputized as a DEA Task Force Officer during part of the investigation. These seven individuals are the individual appellees in the instant suit.
All targets of the Mansfield controlled buys were selected either by Bray or RCSO. The controlled buys resulted in numerous arrests and indictments. Robertson, Lovett, Spires, Matthews, Brooks, and Brown were among those indicted.
Lucas was the case agent who testified before the grand jury concerning Robertson, Lovett, Spires, Matthews, Brooks, and Brown. He testified about the corroborative measures generally used to substantiate Bray’s information and to supervise Bray’s controlled purchases. These included:
• criminal history checks on each suspect;
• driver’s license checks on each suspect;
• searches of Bray’s person and vehicle prior to a controlled purchase to confirm that he did not have drugs or money;
• tape-recorded phone calls to the suspects to set up buys;
• copies of serial numbers of the buy money so that if a suspect was arrested, officers could confirm that Bray used money supplied by law enforcement to make the controlled purchase;
• audio surveillance via a transmitter;
• visual surveillance of the purchases, which included watching Bray enter and exit the buy location and watching the drug transaction take place if visible;
• meeting Bray after the buy at a predetermined location to recover the drugs and recording device;
• re-searching Bray and his vehicle to make sure he did not steal drugs or money; and
• in certain cases, undercover participation by Lucas or Ansari in the drug transaction.
Lucas also testified about specific controlled purchases Bray made from appellants. On the basis of this information, a federal grand jury returned an indictment and later a superseding indictment against appellants. On November 9, 2005, pursuant to the initial indictment, a judge issued warrants for appellants’ arrests.
B.
Corruption pervaded the Mansfield Investigation. Following the completion of the investigation, Bray, while in jail for an unrelated homicide, disclosed that he had abused his position as an informant. The evidence in this case strongly indicates that, as to some arrestees, law enforcement knew of, and even participated in, Bray’s misdeeds. Appellants produced copious evidence of wrongdoing throughout the wider investigation. We need not detail all the evidence in this case to emphasize that law enforcement conducted itself inappropriately. Nevertheless, we provide some context for appellants’ claims.
Appellants produced evidence indicating that Bray, while working as a confidential informant, framed innocent individuals, stole money and drugs from law enforcement, and dealt his own drugs on the side. Appellants also produced evidence that officers altered evidence to corroborate Bray and that certain appellees lied to prosecutors on Bray’s behalf.
[612]*612Bray used stand-ins to frame innocent individuals, and appellees supported Bray’s false identifications of these individuals. For example, a stand-in was used to frame appellants’ former co-defendant Dwayne Nabors. Metcalf has admitted that he lied during Nabors’s criminal trial, including admitting to a false identification of Nabors. Ansari also falsely identified Nabors in the alleged drug transaction. Lucas and Metcalf lied to the prosecutor about whether there was video taken of the transaction, although Metcalf himself had operated the video camera.
Bray used the controlled buys to steal money and drugs. Appellees were aware of this fact yet continued to use Bray as an informant. On one occasion, Verhiley and Ansari caught Bray stealing money given to him for a drug buy. On another occasion, Bray accepted a Buick Cutlass (a car) in lieu of some of the money that was supposed to be paid as part of the drug deal. In effect, Bray was shorting the government the value of the car. Bray, however, was caught on appellees’ recording discussing the “Cutty.” When Bray was questioned about the conversation, he claimed it was a comment about a “Caddy” (Cadillac) that he had been interested in purchasing, but Lucas stepped in on Bray’s behalf and asserted that “Cutty” was another term for drugs.
Efforts to corroborate Bray’s information were stymied by Bray, and law enforcement disregarded accepted protocol. For example, the first step in a controlled buy was typically a controlled phone call to the target. Appellants produced evidence indicating that Bray dialed identical telephone numbers for unrelated suspects and lied about which suspects he was calling and that the official reports did not accurately reflect the phone conversations Bray had. Bray at times turned off his wireless transmitter during buys. Metcalf also admitted that “the manner in which the Webb deal was conducted violated DEA procedures” and “was not the way that a standard deal should go.”
Almost none of appellants’ evidence, however, relates to their own controlled buys, or their subsequent arrests and prosecutions. Only Lovett and Robertson even suggested any impropriety in drug buys involving appellants. At Lucas’s criminal trial, discussed at greater length below, Bray testified that he supplied Lo-vett with the drugs that Lovett allegedly sold to Bray in order to frame Lovett for the sale. Robertson testified that Bray set him up in a manner similar to Lovett. This story was confirmed by Bray at Lucas’s trial. Lucas claims that he was not aware of either set-up. And Bray testified that no law enforcement officials, including Lucas, were involved in or aware of his deceptions.
C.
As a result of Bray’s admissions, the investigation fell apart. On December 20, 2007, Bray pled guilty to two counts of perjury and five counts of deprivation of civil rights. Bray admitted to falsely identifying several targets as having participated in drug transactions and to perjuring himself at trial by deliberately misidentifying people. Bray’s plea, however, did not implicate any of the appellants in this case.
In May 2009, Metcalf was charged with a criminal civil rights violation for his actions and testimony related to Dwayne Nabors. Metcalf pled guilty to presenting false evidence against Nabors at trial and admitted that he falsely identified Nabors as a participant in a drug deal. Metcalfs plea did not directly implicate appellants in this case.
Lucas was indicted for obstruction of justice, making false statements, perjury, [613]*613and deprivation of civil rights for his role in the Mansfield Investigation. Bray testified as a witness for the government. In his testimony, Bray stated that he did not fabricate evidence in the transactions involving appellants Matthews, Spires, or Brooks, and that the purchases of drugs from these individuals were legitimate. Bray also stated that no law enforcement officials, including Lucas and Ansari, were involved in or aware of his deceptions. Bray claimed that he initially falsely told authorities that Lucas and Ansari were complieit in his actions, specifically those involving Geneva France and Joshawa Webb, but Bray later repudiated that statement. A jury acquitted Lucas of all eighteen counts.
D.
Based on Bray’s guilty plea, the federal government reviewed the evidence in the Mansfield arrests. The government determined that “Bray was an essential witness to the charges for which they were either convicted or pled guilty.” The government further concluded that “Bray’s illegal conduct was so pervasive and his credibility so tainted by his guilty plea” that appellants and the other Mansfield Investigation defendants were entitled to withdraw their guilty pleas. The government recommended the dismissal of all criminal charges against appellants, notwithstanding its acknowledgment that many of the appellants “made voluntary statements to law enforcement admitting their roles in the distribution of crack cocaine in the greater Mansfield area.” The withdrawal of appellants’ guilty pleas and the dismissal of the charges against them gave rise to the instant suit.
E.
There are six appellants in this case: Johnny Roberston, Nolan Lovett, Arrico Spires, Charles Matthews, Marlon Brooks, and Tyron Brown.1 Each appellant was a target of the Mansfield Investigation and eventually pled guilty to various drug offenses.
Appellants filed suit in the United States District Court for the Northern District of Ohio on May 20, 2008. They alleged Fourth Amendment violations of false arrest, malicious prosecution, and fabrication of evidence under 42 U.S.C. § 1988 against the state officers, and parallel claims under 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), against the DEA appellees; civil conspiracy under § 1983 and Bivens; and violations of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).2 Appellants also brought claims against Richland County and the City of Cleveland under Monell v. Department of Social Services of New York, 436 U.S. 658, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978). Appellants brought Ohio common-law tort claims of false arrest, malicious prosecution, intentional infliction of emotional distress, and conspiracy against the law enforcement officers. The United States was substituted as the proper party to defend the Ohio common-law tort claims on behalf of the federal appellees Lucas, Cross, Ansari, and [614]*614Verhiley.3
Following appellees’ motions for summary judgment, the district court granted in part appellants’ requests for additional discovery, limiting further discovery to the issue of qualified immunity. The district court allowed appellants to depose appel-lees Verhiley, Cross, Mayer, Faith, and Metcalf, as well as two non-defendant law enforcement officers.
The district court then granted the individual appellees’ motions for summary judgment on the basis of qualified immunity. Finding no underlying constitutional violations, the district court granted Rich-land County’s and the City of Cleveland’s motions to dismiss appellants’ Monell claims. The district court also granted the government’s motion to dismiss all claims against the United States.
II.
We review a district court’s grant of summary judgment on the basis of qualified immunity de novo. Dixon v. Univ. of Toledo, 702 F.3d 269, 273 (6th Cir.2012). Summary judgment is proper where no genuine issue of material fact exists and the moving party is entitled to judgment as a matter of law. Fed.R.Civ.P. 56(a). In considering a motion for summary judgment, this court construes all reasonable inferences in favor of the nonmoving party. Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986).
Appellants asserted numerous claims under 42 U.S.C. § 1983 and Bivens, 403 U.S. at 392, 91 S.Ct. 1999. We review Bivens and § 1983 actions under the same legal principles, except for the requirement of federal action under Bivens and state action under § 1983. A plaintiff must prove two elements to prevail on either type of claim: (1) that he or she was deprived of. a right secured by the Constitution or laws of the United States; and (2) that the deprivation was caused by a person acting under color of law. Bivens, 403 U.S. at 392, 91 S.Ct. 1999; Marcilis v. Twp. of Redford, 693 F.3d 589, 595 (6th Cir.2012); Redding v. St. Eward, 241 F.3d 530, 532 (6th Cir.2001).
The district court found, and it is undisputed, that appellees acted under color of law. The issue, then, is whether appellants were deprived of constitutionally or federally protected rights.
The district court awarded the individual appellees summary judgment on the ground that each was entitled to qualified immunity. The doctrine of qualified im[615]*615munity is an affirmative defense to Bivens and § 1983 claims. Binay v. Bettendorf, 601 F.3d 640, 647 (6th Cir.2010).
There are two general steps to a qualified immunity analysis. The court must determine whether “the facts alleged show the officer’s conduct violated a constitutional right” and whether that right was “clearly established.” Saucier v. Katz, 533 U.S. 194, 201-02, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001). Under Pearson v. Callahan, we may address either question first. 555 U.S. 223, 236, 129 S.Ct. 808, 172 L.Ed.2d 565 (2009).4 “Once the qualified immunity defense is raised, the burden is on the plaintiff to demonstrate that the officials are not entitled to qualified immunity.” Binay, 601 F.3d at 647 (internal quotation marks omitted).
It is axiomatic that both to establish a prima facie case for liability and to overcome a qualified immunity defense, a plaintiff must demonstrate that his or her own rights were violated. For example, to prevail on their false arrest claims, appellants were required to prove that the officers lacked probable cause to arrest them. Likewise, “[g]overnment officials, including police officers, are immune from civil liability unless, in the course of performing their discretionary functions, they violate the plaintiffs clearly established constitutional rights.” Jones v. Byrnes, 585 F.3d 971, 974 (6th Cir.2009) (emphasis added). Not only is this analysis individualized on the plaintiffs side of the equation, it is equally individualized on the defendant’s side. A critical aspect of the § 1983 and Bivens universe is that to be held liable, a plaintiff must demonstrate “that each Government-official defendant, through the official’s own individual actions, has violated the Constitution.” Ashcroft v. Iqbal, 556 U.S. 662, 676, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009). Simply put, to establish liability and to overcome a qualified immunity defense, an individual must show that his or her own rights were violated, and that the violation was committed personally by the defendant.
Appellants adduced substantial evidence of general government wrongdoing. But as discussed below, appellants’ claims fail at step one because appellants failed to produce evidence that their own rights were violated.
1.
Lucas is the central figure in this case. Lucas’s testimony before the grand jury was integral to the commencement of criminal proceedings against appellants. The grand jury issued an indictment on the basis of his testimony, which led to arrest warrants and eventually appellants’ arrests. Appellants’ claims against the remaining individual appellees assert either that the appellees influenced Lucas’s testimony or that they knew Lucas testified falsely. Therefore, we begin our analysis with Lucas.
Appellants’ primary claims against Lucas are for malicious prosecution and [616]*616unlawful detention. These claims can be addressed together under the “umbrella of a ‘malicious prosecution’ claim.” Gregory v. City of Louisville, 444 F.3d 725, 747 (6th Cir.2006). Our cases “recognize[ ] a separate constitutionally cognizable claim of malicious prosecution under the Fourth Amendment, which encompasses wrongful investigation, prosecution, conviction, and incarceration.” Sykes v. Anderson, 625 F.3d 294, 308 (6th Cir.2010) (internal quotation marks and alterations omitted). “The tort of malicious prosecution is entirely distinct from that of false arrest, as the malicious-prosecution tort remedies detention accompanied not by absence of legal process, but by wrongful institution of legal process.” Id. (internal quotation marks omitted).
To succeed on a Fourth Amendment malicious prosecution claim under § 1983 or Bivens, a plaintiff must prove the following: (1) a criminal prosecution was initiated against the plaintiff and the defendant made, influenced, or participated in the decision to prosecute; (2) there was no probable cause for the criminal prosecution; (3) as a consequence of the legal proceeding, the plaintiff suffered a deprivation of liberty apart from the initial seizure; and (4) the criminal proceeding was resolved in the plaintiffs favor. Id. at 308-09. The basis of appellants’ claim is that Lucas caused their prosecutions and their detentions unlawfully to continue by fabricating and withholding evidence, “the absence of either or both of which would have dissolved probable cause.” Gregory, 444 F.3d at 747.5
In an unpublished opinion arising from the Mansfield Investigation, we reiterated: “As a general rule, the finding of an indictment, fair upon its face, by a properly constituted grand jury, conclusively determines the existence of probable cause. However, an exception applies where the indictment was obtained wrongfully by defendant police officers who knowingly presented false testimony to the grand jury.” Mott v. Mayer, 524 Fed.Appx. 179, 187 (6th Cir.2013) (internal citations, quotation marks, and alterations omitted) (citing Cook v. McPherson, 273 Fed.Appx. 421, 424 (6th Cir.2008); Peet v. City of Detroit, 502 F.3d 557, 566 (6th Cir.2007); Barnes v. Wright, 449 F.3d 709, 716 (6th Cir.2006)). This exception also covers officers who testify with a reckless disregard for the truth. Cf. Sykes, 625 F.3d at 305.
Lucas testified to a host of corroborative procedures used in controlled buys throughout the wider Mansfield Investigation. He testified generally that in “[ejach one of these buys” these corroborative procedures were used. Thus, his testimony permits an inference that these corroborative measures were used as to each appellant. Because Lucas’s testimony permitted an inference that appropriate corroborative procedures were used during the drug buys involving each appellant, appellants bore the burden of producing evidence that this was not the case; otherwise, Lucas’s testimony was not false as to each appellant.
The crux of appellants’ argument is that Lucas’s testimony to the grand jury contained knowing falsehoods because he did not tell the grand jury that information [617]*617obtained from the confidential informant, Bray, was suspect based on Bray’s criminal history, theft of drugs and money belonging to law enforcement, and fabrication of evidence through the use of stand-ins or staged drug buys to frame individuals other than the appellants here. Appellants have presented no evidence that Lucas falsely testified to the officers’ efforts to corroborate Bray’s information about them.6 That is, appellants cannot overcome the presumption of probable cause, see Mott, 524 Fed.Appx. at 186-87, and therefore cannot show that their own constitutional rights were violated.
Lucas also testified that each appellant participated in an illegal drug transaction. Appellants produced some evidence that Lucas’s testimony about the controlled buys involving Lovett and Robertson was false. Bray testified at Lucas’s criminal trial that he supplied Lovett with the drugs that Lovett sold to Bray on that occasion. Appellants produced no evidence, however, that Lucas either knew this to be the case or was reckless as to that fact when he testified before the grand jury. Thus, even if Lucas did testify to a falsity regarding the Lovett controlled buy, appellants have not produced evidence demonstrating that Lucas did so knowingly or recklessly.
As to the Robertson controlled purchase, appellants have similarly failed to produce evidence that Lucas knew or was reckless to 'the fact that Bray was setting up Robertson. Robertson now claims that he did not participate in the October 2005 transaction. But appellants have not produced evidence demonstrating that Lucas knowingly or recklessly testified to the fact that Robertson participated in the transaction. Lucas was the surveillance agent on the case and thus was not immediately present during the buy. Moreover, Lucas has stated that Ansari informed him that Ansari observed Robertson receive money for his participation in the transaction. The evidence indicates that Lucas, as the surveilling agent, believed that appropriate corroborative procedures were used and that Robertson participated in the transaction. Neither Robertson’s nor Bray’s testimony suggests that Lucas knew Robertson was being framed.7
Lucas is entitled to qualified immunity on appellants’ malicious prosecution and unlawful detention claims because appellants produced no evidence that Lucas violated their constitutional rights.8
[618]*618b.
Appellants also brought a false arrest claim against Lucas. The proper defendants in an action under § 1983 or Bivens are the law enforcement officers who were personally involved in the incident alleged to have resulted in a violation of the plaintiffs civil rights. See Gregory, 444 F.3d at 759. There is no suggestion that Lucas was involved in appellants’ arrests. And even on a theory that Lucas caused appellants’ arrests by providing grand jury testimony, appellants’ claim would fail because, as discussed above, appellants have not established that Lucas gave false testimony. Accordingly, Lucas is entitled to qualified immunity on appellants’ false arrest claim.
2.
We turn now to the remaining individual appellees. Appellants brought false arrest claims against the remaining individual ap-pellees. As discussed below, to prevail, appellants were required to show that they relied on a warrant that they knew issued without probable cause. Thus, these claims in reality depend on their production of evidence that Lucas lied or was reckless in respect to them before the grand jury, as the warrant was issued on the basis of the grand jury’s finding of probable cause.9 And appellees could hardly have known or should have known that Lucas testified falsely if he in fact did not do so. Nevertheless, it is at least theoretically possible that an officer’s state of mind about a warrant — i.e., knowledge that it was issued without probable cause — was such that his execution of the warrant violated an individual’s constitutional rights.
The Fourth Amendment protects against unreasonable searches and seizures and requires that arrest warrants be issued only upon a showing of probable cause. U.S. Const, amend. IV. To state a Fourth Amendment false arrest claim, a plaintiff must “prove that the arresting officer lacked probable cause to arrest the plaintiff. An arrest pursuant to a facially valid warrant is normally a complete defense to a federal constitutional claim for false arrest or false imprisonment made pursuant to § 1983.” Voyticky v. Vill. of Timberlake, 412 F.3d 669, 677 (6th Cir.2005) (internal citation omitted). Indeed, “it has been long settled that the finding of an indictment, fair upon its face, by a properly constituted grand jury, conclusively determines the existence of probable cause.” Barnes, 449 F.3d at 716 (internal quotation marks omitted).
[619]*619As above, an exception exists. As the Seventh Circuit held in Juriss v. McGowan, there is
a recognized exception for situations where officers responsible for bringing about an unlawful arrest knew that the arrest warrant had issued without probable cause; this is particularly true of officers who knew that those who obtained the warrant had deceived the authorizing body. Under these circumstances, even a facially valid arrest warrant does not shield otherwise unreasonable conduct.
957 F.2d 345, 350-51 (7th Cir.1992) (internal citations omitted).
As probable cause was established on the basis of the grand jury indictment, appellants bore the burden of producing evidence demonstrating that the remaining individual appellees either knew or were reckless in not knowing that Lucas gave false 'testimony that tainted the finding of probable cause. Appellants failed to present any particularized evidence demonstrating that the individual appellees relied on an arrest warrant they knew had issued without probable cause. Nor did appellants produce evidence demonstrating that any individual appellee influenced Lucas’s grand jury testimony, causing him to lie to or mislead the grand jury, thereby leading to appellants’ arrests. Therefore, the district court did not err in concluding that the remaining individual appellees were entitled to qualified immunity on this claim.10
Appellants also asserted malicious prosecution, unlawful detention, and fabrication of evidence claims against the remaining appellees. Appellants produced no evidence that the appellees influenced Lucas’s grand jury testimony, thereby causing appellants’ prosecutions and detentions. And because there was probable cause to arrest and detain appellants, they cannot prevail on their fabrication of evidence claim as they were not wrongfully seized. Appellees were therefore entitled to qualified immunity on these claims as well.
3.
Appellants assert that the district court erred in holding that their Brady claims were foreclosed by the Supreme Court’s holding in United States v. Ruiz, 536 U.S. 622, 122 S.Ct. 2450, 153 L.Ed.2d 586 (2002). A constitutional tort claim on the basis of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), is properly construed as a § 1983 or Bivens claim. See Sykes, 625 F.3d at 319. Such a claim is subject to a qualified immunity defense. See Gregory, 444 F.3d at 745.
This case, appellants assert, lies at the intersection of two different Brady doctrines: Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Brady v. United States, 397 U.S. 742, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970).11 Brady v. Maryland familiarly holds that prosecutors must turn over favorable evidence to the accused when the evidence is material either to guilt or punishment; wrongful withholding is a violation of the right to due process. 373 U.S. [620]*620at 89, 83 S.Ct. 1194. Evidence is material when “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Kyles v. Whitley, 514 U.S. 419, 438-34, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (internal quotation marks omitted). This obligation extends to evidence that is favorable to the accused “either because it is exculpatory, or because it is impeaching.” Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Law enforcement is also part of the Brady universe. “[B]ecause the police are just as much an arm of the state as the prosecutor, the police inflict the same constitutional injury when they hide, conceal, destroy, withhold, or even fail to disclose material exculpatory information.” Moldowan v. City of Warren, 578 F.3d 351, 379 (6th Cir.2009).
In Ruiz, the Supreme Court held that “the Constitution does not require the Government to disclose material impeachment evidence prior to entering a plea agreement with a criminal defendant.” 536 U.S. at 633, 122 S.Ct. 2450. This is so for three reasons. First, “impeachment information is special in relation to the fairness of a trial, not in respect to whether a plea is voluntary.” Id. at 629, 122 S.Ct. 2450. Second, the Constitution does not require that a defendant entering into a plea agreement have complete knowledge of the circumstances surrounding the plea; a court is permitted to accept a guilty plea “despite various forms of misapprehension under which a defendant might labor.” Id. Third, the due process considerations that motivated Brady’s disclosure requirement for impeachment information do not apply as strongly in the plea context. Id. at 631, 122 S.Ct. 2450. A constitutional obligation that the prosecutor disclose impeachment material before plea bargaining, the Court reasoned, “could seriously interfere with the Government’s interest in securing those guilty pleas that are factually justified, desired by defendants, and help to secure the efficient administration of justice.” Id.
The Brady v. United States line of doctrine holds that a guilty plea must be “a voluntary and intelligent choice among the alternative courses of action open to the defendant.” North Carolina v. Alford, 400 U.S. 25, 31, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970). In Brady v. United States, the Supreme Court stated that “misrepresentations or other impermissible conduct by state agents” might justify the withdrawal of a defendant’s guilty plea. 397 U.S. 742, 757, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970).
Appellants allege that the government made “dishonest disclosures tricking them into pleading guilty.” Prior to each appellant’s plea, they were informed that “[t]he attorney for the government has no knowledge of exculpatory evidence material to guilt or innocence of the defendant.” This, appellants contend, amounts to a material misrepresentation in violation of Brady v. Maryland and makes their pleas involuntary under Brady v. United States.
We need not reconcile these two lines of doctrine and answer the question whether misleading Brady disclosures at the plea bargaining stage violate either Brady v. Maryland or Brady v. United States. In this case, appellants were not tricked into pleading guilty. The prosecutor informed each appellant, “The attorney for the government has no knowledge of exculpatory evidence material to guilt or innocence of the defendant.” The prosecutor did not state that there was no Brady material, just that he did not know of any. There is no evidence that this statement was false, and thus, at least so far as the prosecutor was concerned, there was no false or misleading Brady disclosure.
[621]*621To the extent the failure to disclose this evidence can be attributed to appellees, as it must be, see Iqbal, 556 U.S. at 676, 129 S.Ct. 1937, their alleged misfeasance was in failing to inform the prosecutor of Brady material in their possession before the prosecutor made the disclosure. On this score, appellees are entitled to qualified immunity.
Whatever rights appellants had to receive exculpatory evidence prior to entering their pleas was not clearly established. The Supreme Court recently stated that “the contours of a right are sufficiently clear [where] every reasonable official would have understood that what he is doing violates that right.” Ashcroft v. al-Kidd, — U.S.-, 131 S.Ct. 2074, 2083, 179 L.Ed.2d 1149 (2011). “If the law did not put the officer on notice that his conduct would be clearly unlawful, summary judgment based on qualified immunity is appropriate.” Saucier, 533 U.S. at 202, 121 S.Ct. 2151.
Ruiz established that impeachment material need only be disclosed for trial. See United States v. Wells, 260 Fed.Appx. 902, 903-04 (6th Cir.2008). Appellants contend that the evidence at issue was exculpatory and therefore not covered by the rule set forth in Ruiz. We have not yet had occasion to determine whether Ruiz applies to exculpatory Brady material, a question that has caused some disagreement among our sister circuits. Compare United States v. Ohiri, 133 Fed.Appx. 555, 562 (10th Cir.2005) (“[T]he Supreme Court did not imply that the government may avoid the consequence of a Brady violation if the defendant accepts an eleventh-hour plea agreement while ignorant of withheld exculpatory evidence in the government’s possession.”) and McCann v. Mangialardi, 337 F.3d 782, 788 (7th Cir.2003) (“Ruiz indicates a significant distinction between impeachment information and exculpatory evidence of actual innocence.”), with Friedman v. Rehal, 618 F.3d 142, 154 (2d Cir.2010) (“[T]he Supreme Court has consistently treated exculpatory and impeachment evidence in the same way for the purpose of defining the obligation of a prosecutor to provide Brady material prior to trial, and the reasoning underlying Ruiz could support a similar ruling for a prosecutor’s obligations prior to a guilty plea.”) (internal citations omitted) and United States v. Conroy, 567 F.3d 174, 179 (5th Cir.2009) (“Ruiz never makes such a distinction nor can this proposition be implied from its discussion.”).
Nor does our own caselaw support appellants’ argument that they had a clearly established right to receive exculpatory Brady material prior to plea bargaining. We have held that “[i]n general, the principles announced in Brady do not apply to a tardy disclosure of exculpatory information, but to a complete failure to disclose. If previously undisclosed evidence is disclosed ... during trial, no Brady violation occurs unless the defendant has been prejudiced by the delay in disclosure.” United States v. Word, 806 F.2d 658, 665 (6th Cir.1986) (internal citation omitted). Therefore, every reasonable officer in appellees’ positions would know that they were under an obligation to present Brady material to the prosecutors “in time for its effective use at trial.” United States v. Bencs, 28 F.3d 555, 561 (6th Cir.1994). And in Campbell v. Marshall, we held that a prosecutor’s failure to disclose arguably exculpatory Brady material prior to plea bargaining did not render the defendant’s guilty plea involuntary where a factual basis for the plea was established at the plea proceeding. 769 F.2d 314, 318, 323-24 (6th Cir.1985).
Accordingly, we hold that appellees were under no clearly established obligation to disclose exculpatory Brady material to the [622]*622prosecutors in time to be put to effective use in plea bargaining. We do not decide whether appellants have a constitutional right to receive exculpatory Brady material from law enforcement prior to entering into a plea agreement.
4.
Appellants assert that the district court erred in granting summary judgment to appellees on their conspiracy claims. A civil conspiracy claim under § 1983 or Bivens lies where there is “an agreement between two or more persons to injure another by unlawful action.” Revis v. Meldrum, 489 F.3d 273, 290 (6th Cir.2007). To prevail on such a claim in this context, appellants must demonstrate “that (1) a single plan existed, (2) the conspirators shared a conspiratorial objective to deprive the plaintiffs of their constitutional rights, and (3) an overt act was committed” in furtherance of the conspiracy that caused the injury. Id.
Plaintiffs are not required to prove an express agreement among all the conspirators, and “[e]ach conspirator need not have known all of the details of the illegal plan or all of the participants involved.” Hooks v. Hooks, 771 F.2d 935, 944 (6th Cir.1985). In opposing a motion for summary judgment, plaintiffs are entitled to “rely on circumstantial evidence to establish an agreement among the conspirators.” Hensley v. Gassman, 693 F.3d 681, 695 (6th Cir.2012). Nevertheless, “[i]t is well-settled that conspiracy claims must be pled with some degree of specificity and that vague and conclusory allegations unsupported by material facts will not be sufficient to state such a claim under § 1983” or Bivens. Gutierrez v. Lynch, 826 F.2d 1534, 1538 (6th Cir.1987) (affirming grant of summary judgment where “Plaintiffs allegations lack[ed] the requisite material facts and specificity necessary to sustain a conspiracy claim”).
The district court granted summary judgment on two grounds: appellants failed to produce any specific evidence that the defendants shared a single plan and a common objective, and appellants failed to prove that any of their constitutional rights were violated. On appeal, appellants again fail to point to any specific evidence of a common plan or objective. The district court therefore did not err in granting summary judgment on appellants’ conspiracy claims.
III.
Switching to appellants’ claims against Richland County and the City of Cleveland, appellants argue that the district court erred in dismissing their Monell claims. Monell holds that municipalities may be held liable for the constitutional violations of their employees only where the municipality’s policy or custom led to the violation. 436 U.S. at 694-95, 98 S.Ct. 2018. There can be no liability under Monell without an underlying constitutional violation. See Scott v. Clay Cnty., Tenn., 205 F.3d 867, 879 (6th Cir.2000). Finding no underlying constitutional violation, the district court dismissed appellants’ Monell claims.
We affirm the district court and agree with its reasoning with respect to all claims against Richland County and the City of Cleveland except for the Brady claims. With respect to the Brady claims, we affirm the district court but on other grounds.
Appellants’ Monell claims are before this court on a motion to dismiss. Appellants’ amended complaint alleged:
Plaintiffs’ injuries were proximately caused by policies and practices on the part of Defendants Richland County and [623]*623the City of Cleveland to pursue wrongful convictions through profoundly flawed investigations and unlawful searches and seizures. In this way, these Defendants violated Plaintiffs’ rights by maintaining policies and practices that were the moving force driving the foregoing constitutional violations.
Appellants do not plead that appellees maintained a policy or custom of refusing to turn over exculpatory or impeachment evidence. Appellants’ nebulous assertions of wrongdoing in the form of “flawed investigations” and “unconstitutional searches and seizures” do not pertain to the alleged Brady violations; rather, appellants assert constitutional violations in the conduct leading up to but not including the disclosure of exculpatory evidence. Rule 8 requires that a plaintiffs pleadings “give the defendant fair notice of what the claim is and the grounds upon which it rests.” Bell Atlantic v. Twombly, 550 U.S. at 544, 555, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007) (internal quotation marks and alterations omitted). Appellants’ complaint, which fails to claim that their rights were violated by a policy or custom of refusing to turn over exculpatory or impeachment evidence, cannot be said to have given appellees fair notice of this claim. As this deficiency is manifest from the face of appellants’ complaint, we affirm the district court’s dismissal of appellants’ Monell claims alleging Brady violations against Richland County and the City of Cleveland.
IV.
“The scope of discovery is within the sound discretion of the trial court, and a ruling by the trial court limiting or denying discovery will not be cause for reversal unless an abuse of discretion is shown.” S.S. v. E. Ky. Univ., 532 F.3d 445, 451 (6th Cir.2008) (internal alterations and quotation marks omitted). In the context of qualified immunity, deferential review of a district court order limiting discovery is imperative. “The philosophy behind the doctrine of qualified immunity ‘is a desire to avoid the substantial costs imposed on government, and society, by subjecting officials to the risks -of trial.’ ” Skousen v. Brighton High Sch., 305 F.3d 520, 526 (6th Cir.2002) (quoting Vaughn v. U.S. Small Bus. Admin., 65 F.3d 1322, 1326 (6th Cir.1995)). Thus, the Supreme Court has “repeatedly ... stressed the importance of resolving immunity questions at the earliest possible stage in litigation.” Pearson v. Callahan, 555 U.S. 223, 232, 129 S.Ct. 808, 172 L.Ed.2d 565 (2009) (internal quotation marks omitted).
Discovery is disfavored in this context, but “limited discovery may sometimes be necessary before the district court can resolve a motion for summary judgment based on qualified immunity.” Crawford-El v. Britton, 523 U.S. 574, 593 n. 14, 118 S.Ct. 1584, 140 L.Ed.2d 759 (1998). In CrawforcL-El, after noting the “many options” a district court judge has in conducting discovery in a qualified immunity case, the Supreme Court explained: “Of course, the judge should give priority to discovery concerning issues that bear upon the qualified immunity defense, such as the actions that the official actually took, since that defense should be resolved as early as possible.” Id. at 599-600, 118 S.Ct. 1584.
Appellants assert that the district court erred when it permitted the appellants to depose certain appellees but limited the depositions to the qualified immunity issue. The district court, after briefing on the issue, authorized three-hour depositions of Verhiley, Cross, Mayer, Faith, Metcalf, and two non-defendant law enforcement officers. This was after appellees had vol[624]*624untarily disclosed a tremendous number of documents. As the district court stated in denying appellants’ request for additional discovery:
Plaintiffs already have in their possession abundant evidence concerning the Mansfield operation and their claims. This evidence includes over 4,000 pages of trial transcript and more than 22,000 pages of exhibits from Special Agent Lucas’ criminal trial, and testimony in the cases of United States v. Nabors ... and United States v. France. Plaintiffs possess the entire files of the: (1) United States Attorney’s office in Cleveland; (2) DEA; and (3) RCSO. All proffers of the Mansfield defendants have been provided to Plaintiffs, in addition to audio and video recordings of the Mansfield transactions, as well as transcripts of the recordings. Plaintiffs have the deposition of Defendant Ansari and answers to 20 interrogatories propounded with the permission of the Court in the companion case Westerfield v. Lucas.
The district court followed the Supreme Court’s dictates on discovery in qualified immunity cases precisely. The district court, in its discretion, limited discovery to issues that had a direct bearing “upon the qualified immunity defense, such as the actions that the officials] actually took.” Crawford-El, 523 U.S. at 600, 118 S.Ct. 1584. Because a plaintiff cannot sustain a § 1983 or Bivens claim without a showing of personal responsibility on the part of the defendant, see Iqbal, 556 U.S. at 676, 129 S.Ct. 1937, appellants’ Fourth Amendment claims — and the accompanying qualified immunity defenses — turned fil large part on the individual actions of the defendants in this case. The same is true for the alleged Brady violations. Finally, as to appellants’ argument that the conspiracy claims necessitated information about the wider investigation, no conspiracy can exist without the appellees’ participation. The district court therefore did not err when it limited discovery to information pertaining to appellees’ conduct.12
y.
Because appellants failed to establish that their rights were violated, we affirm the district court’s judgment with respect to the individual appellees on all but appellants’ Brady claims. With respect to the Brady claims, we affirm because appellants did not have a clearly established right to receive allegedly exculpatory Brady material prior to entering their pleas. Being that appellants failed to establish constitutional violations, we affirm the district court’s judgment with respect to Richland County and the City of Cleveland except with respect to the district court’s dismissal of appellants’ Brady claims under Monell, which we affirm because appellants failed to allege adequately a policy or custom of withholding Brady material. Finally, we affirm the district court’s judgment with respect to additional discovery.