Defamation with Bayesian Audiences

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Yonathan A. Arbel & Murat C. Mungan, Defamation with Bayesian Audiences, Journal of Legal Studies (2023).

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Defamation with Bayesian Audiences analyzes how strictly law should regulate false defamatory statements when audiences update their beliefs in response to legal rules and judicial error. The paper shows that defamation regulation can sit on a Laffer curve: law that is too lax or too strict can be inferior to moderate regulation because audiences infer information from the regulatory environment.

What this paper is about:

Defamation with Bayesian Audiences analyzes how strictly law should regulate false defamatory statements when audiences update their beliefs in response to legal rules and judicial error. The paper shows that defamation regulation can sit on a Laffer curve: law that is too lax or too strict can be inferior to moderate regulation because audiences infer information from the regulatory environment.

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This work is relevant to Defamation And Speech, Private Law And Market Institutions. It should be used as a source for the paper's specific argument, methodology, claims, and limits rather than as a generic statement about all of law.

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Research Paper Series Research Paper No. 23–66 Defamation with Bayesian Audiences

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This work is relevant when answering questions about Defamation And Speech, Private Law And Market Institutions.

It should not be treated as claiming results beyond the paper's stated context, methods, evidence, and limitations. Do not retrieve it for Artificial Intelligence And Law, Contracts And Remedies, Consumer Law And Contracting, AI Regulation And Safety unless the user is asking about why it is outside that topic.

The most important takeaway is: Defamation with Bayesian Audiences analyzes how strictly law should regulate false defamatory statements when audiences update their beliefs in response to legal rules and judicial error. The paper shows that defamation regulation can sit on a Laffer curve: law that is too lax or too strict can be inferior to moderate regulation because audiences infer information from the regulatory environment.

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Defamation law changes the credibility audiences assign to speech, not merely speakers’ incentives and targets’ compensation

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 1–2, that the strictness of defamation law is itself a credibility cue. Audiences infer whether surviving negative speech is cheap, risky, or selectively deterred and then decide whether to trade, collaborate, or socialize with the target. A two-party framework centered on speaker and target therefore misses a third-party belief channel through which liability changes harm. This is significant because the effect of a statement depends on whether listeners believe and act on it. It connects to Bayesian updating, credibility, audience effects, defamation damages, cheap talk, and third-party behavior.

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A useful defamation model must combine Bayesian audiences, judicial error, and an upper bound on recoverable damages

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 2–3, that three realistic features jointly determine optimal strictness: listeners update beliefs from the legal environment, courts sometimes impose or withhold liability incorrectly, and constitutional or wealth constraints may cap damages. The model follows a privately informed speaker, a good or bad target, an audience choosing whether to interact, and a target deciding whether to sue. This is significant because omitting any one feature can reverse the policy result. It connects to Bayesian games, Type I error, Type II error, judgment-proof defendants, constitutional damages limits, and litigation incentives.

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Intermediate damages can support a separating equilibrium in which speakers truthfully distinguish good targets from bad targets

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 2, that an intermediate range of damages can deter false disparagement of good targets without deterring truthful warnings about bad targets. In that separating equilibrium, audiences believe the speaker, beneficial interactions with good targets occur, harmful interactions with bad targets are avoided, and frivolous suits do not arise. This is significant because moderate liability can make private speech maximally informative. It connects to separating equilibrium, truthful revelation, deterrence, beneficial interaction, harmful interaction, and optimal damages.

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Defamation welfare often follows an inverse-U or Laffer curve because both cheap talk and overpriced talk destroy information

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 2, that lax law permits a flood of false cheap talk, causing rational audiences to discount true and false claims alike and fall back on priors. Excessively strict law makes negative speech too costly, invites frivolous litigation, and chills truthful warnings. Moderate damages occupy the informationally productive middle. This is significant because welfare is nonmonotonic in legal strictness. It connects to Laffer curves, cheap talk, chilling effects, frivolous claims, inverse-U welfare, and information loss.

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When damages cannot reach the separating range, lax law can outperform the strictest feasible law, especially when false accusations cause large losses

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 3–4, that a binding damage cap can make an apparently weak regime welfare superior. The strictest feasible rule lends credibility to negative speech but cannot eliminate all false accusations, so trusted falsehoods block valuable interactions and provoke litigation. Very lax law makes audiences rely more on priors, blunting false claims. The advantage of laxity grows when lost good interactions are especially costly. This is significant because greater reputational harm can counsel less, not more, effective liability. It connects to bounded damages, credibility effects, false negatives, prior beliefs, litigation costs, and counterintuitive regulation.

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Judicial error supplies the reason very large damages become inefficient by inducing frivolous suits and chilling truthful negative speech

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 3–4, that if courts never erred, arbitrarily large feasible damages would deter lies without threatening truthful criticism because bad targets could not profit from suit. Once wrongful liability is possible, high awards induce bad targets to litigate and make even accurate speakers withdraw. Judicial error therefore generates the descending side of the Laffer curve. This is significant because optimal damages depend on adjudicative accuracy, not only the harm from falsehood. It connects to wrongful liability, frivolous litigation, judicial accuracy, excessive damages, truthful criticism, and error costs.

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Treating audiences as naïve hides the possibility that more false speech can reduce the harm of each false statement by diluting credibility

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 3–4, that prior models effectively assume the audience believes every negative statement and that harm is independent of the legal regime. A Bayesian audience instead recognizes that very low damages invite frequent false accusations and discounts them, so lowering damages can reduce the behavioral harm caused by any particular falsehood. This is significant because speech frequency and speech credibility are jointly determined. It connects to naïve audiences, Bayesian skepticism, stigma dilution, equilibrium beliefs, reputational harm, and endogenous credibility.

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The audience-belief framework extends beyond defamation to corporate disclosure, advertising, whistleblowing, and crime reports

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 4, that many fields regulate inaccurate statements made to decision makers. Corporate disclosure affects investors, advertising affects consumers, whistleblower rules affect enforcement agencies, and false-report sanctions affect police. Across them, legal strictness changes both speaker incentives and the informativeness listeners assign to remaining speech. This is significant because belief formation is a general problem of information regulation. It connects to securities disclosure, false advertising, whistleblowers, crime reporting, information law, and credibility design.

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Economic analysis of defamation should join cost-benefit and chilling-effect work with signaling and cheap-talk theory

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 4–6, that rich legal debate has not been matched by a developed economic account of audience response. Earlier work studies investigation incentives, political dishonesty, plaintiff and publisher behavior, and chilling effects, but generally omits Bayesian listeners. Signaling and cheap-talk tools make the audience endogenous and connect legal sanctions to informal reputational consequences. This is significant because methodological choice determines which welfare channels become visible. It connects to Posner, signaling theory, Crawford-Sobel cheap talk, informal sanctions, media incentives, and law and economics.

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The baseline game links a privately informed speaker’s statement to an audience’s interaction choice and a target’s litigation decision

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 6–7, that the essential defamation sequence has three strategic actors. Nature selects a good or bad target and a speaker’s private incentive to block interaction; the informed speaker disparages or does not; the audience updates and chooses whether to interact; and after a disparaging statement causes avoidance, the target may sue. Beneficial interaction occurs only with a good target. This is significant because the model connects speech, belief, conduct, and enforcement in one game. It connects to private information, target quality, representative audiences, interaction decisions, litigation sequence, and Perfect Bayesian equilibrium.

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The speaker’s private benefit from blocking interaction determines willingness to risk litigation and damages

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 6–7, that speakers differ in a privately known gain from making the audience avoid the target. A speaker disparages when this gain exceeds the expected legal price produced by suit probability, liability probability, damages, and litigation cost. Modeling a continuum of speaker incentives permits partial deterrence rather than assuming every speaker reacts identically. This is significant because changing damages selects which motivated speakers remain in the speech pool. It connects to heterogeneous speakers, private benefit, expected sanction, selection effects, partial deterrence, and strategic disparagement.

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Damages operate as a statement-specific policy lever that jointly affects suit incentives and speech incentives under imperfect adjudication

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 7–8, that expected damages can represent nominal, economic, noneconomic, and punitive awards shaped by legal interpretation. A good target has a higher probability of prevailing than a bad target, but judicial error permits both wrongful liability and wrongful nonliability. Increasing damages therefore changes whether each target type sues and whether each speaker type disparages. This is significant because one policy instrument acts on both sides of the litigation threat. It connects to expected damages, judicial error, plaintiff selection, speaker deterrence, litigation costs, and remedy design.

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An equilibrium is informationally effective only when the audience sometimes avoids the target because of the speaker’s message

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 9, that equilibrium existence alone does not show communication matters. They define an effective communication equilibrium as one in which the audience assigns enough informational content to a statement that it sometimes avoids interaction. If the audience takes the same action regardless of speech, communication is ineffective even if speakers and targets choose equilibrium strategies. This is significant because welfare analysis must distinguish strategic consistency from actual information use. It connects to Perfect Bayesian equilibrium, informative communication, audience action, pooling, prior beliefs, and equilibrium refinement.

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Every defamation regime admits an ineffective equilibrium in which audiences ignore speech and act on prior beliefs

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 9, that no damages rule can eliminate all pooling outcomes. If the audience expects speech to reveal nothing and interacts based on its prior, the speaker and target can become indifferent among actions, permitting strategies that confirm the audience’s expectation. Defamation law is irrelevant in that equilibrium because neither messages nor damages change behavior. This is significant because policy changes do not guarantee informative communication merely by changing formal incentives. It connects to multiple equilibria, self-confirming beliefs, pooling, priors, equilibrium selection, and legal irrelevance.

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Extremely low and extremely high damages support only ineffective communication, while moderate damages can support effective communication

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 9–10, that the audience receives no usable signal at either damages extreme. Below the threshold that makes a meritorious suit worthwhile, speakers face no consequence and speech becomes cheap talk. Above the threshold that induces even bad targets to sue and deters every speaker, negative speech disappears as overpriced talk. Between them, some messages remain and are selected by target type. This is significant because informativeness requires neither zero price nor prohibitive price. It connects to Proposition 2, cheap talk, overpriced talk, litigation thresholds, moderate damages, and information transmission.

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In the lower-moderate range, raising damages selectively reduces false disparagement of good targets and the resulting litigation

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 10–12, that low-moderate damages make good targets willing to sue while bad targets still decline. Bad targets are therefore disparaged with certainty, but only speakers with sufficiently high private benefits risk falsely disparaging a good target. Raising damages increases that threshold, reduces false statements, lowers blocked beneficial interactions, and reduces litigation without changing treatment of bad targets. This is significant because initial increases in liability improve both accuracy and cost. It connects to lower-moderate damages, meritorious suits, selective deterrence, false disparagement, litigation reduction, and audience belief.

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Intermediate damages induce complete separation because good targets are never disparaged and bad targets are always disparaged without suing

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 12, that an intermediate range simultaneously deters every false disparagement of a good target and leaves bad targets without an incentive to file frivolous suits. Speakers therefore disparage precisely when they know the target is bad. A negative message conclusively identifies a bad target and its absence identifies a good target. This is significant because private litigation screens both speech and plaintiff type without incurring trial costs. It connects to full separation, truthful warning, frivolous-suit deterrence, target type, perfect information, and private enforcement.

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In the upper-moderate range, frivolous suits by bad targets suppress truthful warnings and cause more harmful interactions

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 12–13, that high-moderate damages make bad targets willing to sue despite weak merits. Speakers with only modest benefits then withhold accurate disparagement to avoid expected liability. Increasing damages further reduces truthful negative speech, causes audiences to interact with more bad targets, and reduces litigation only because speech is chilled. This is significant because fewer lawsuits can coincide with worse information and lower welfare. It connects to upper-moderate damages, frivolous suits, truthful-speech chill, bad interactions, wrongful liability, and selection effects.

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Welfare rises with lower-moderate damages, is maximized across the separating range, and falls with upper-moderate damages

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 14–16, that summing speaker, audience, target, and litigation payoffs yields an inverse-U relationship. Initial increases deter false attacks on good targets and save beneficial interactions and litigation. Intermediate damages produce complete separation and no litigation. Further increases chill valuable warnings about bad targets; the avoided litigation is worth less than the resulting harmful interactions. This is significant because the optimal regime is a range rather than an extreme. It connects to social welfare, inverse-U curve, separating equilibrium, litigation cost, interaction surplus, and nonmonotonic regulation.

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Separating equilibria maximize expected welfare and are attainable only with intermediate damages under the baseline assumptions

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 16, that separation strictly improves on every other equilibrium because the audience interacts if and only if the target is good. No valuable interaction is blocked, no harmful interaction occurs, and the target never needs to litigate. Proposition 3 therefore identifies intermediate damages as the first-best policy whenever those awards are feasible. This is significant because information quality, not the volume of claims or lawsuits, defines the benchmark. It connects to Proposition 3, first-best welfare, complete revelation, interaction matching, intermediate damages, and feasibility.

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Constitutional limits and defendants’ inability to pay can make the first-best separating damages unavailable

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 16–17, that the intermediate award required for complete separation may exceed a constitutional ceiling or the speaker’s wealth. If the cap lies below that threshold, policymakers can choose only ineffective very-low damages or lower-moderate damages that create some credibility while leaving false disparagement. The cap is therefore not a peripheral collection problem; it changes the attainable information regime. This is significant because optimal theory must be evaluated inside real remedial constraints. It connects to judgment-proof speakers, constitutional due process, damage caps, constrained optimization, feasible remedies, and incomplete deterrence.

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Under a binding cap, effective communication trades avoidance of bad interactions for mistaken avoidance of good interactions

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 17–18, that ineffective communication makes the audience follow its favorable prior and interact with both target types. Partially effective capped law blocks every bad interaction but also lets highly motivated speakers falsely block some good ones. Legal credibility therefore substitutes one classification error for another rather than simply improving accuracy. This is significant because the value of enforcement depends on the relative cost of false positive and false negative interaction decisions. It connects to classification error, beneficial transactions, harmful transactions, Bayesian priors, partial revelation, and welfare tradeoffs.

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Above a threshold level of harm to good targets, all feasible effective regimes are weakly worse than leaving the audience to its priors

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 17–18, that Proposition 4 identifies a threshold in the loss from a believed false accusation. With a binding cap, when that loss is sufficiently large, the gains from blocking bad interactions are outweighed by blocked good interactions and litigation. It can then be optimal to select damages so low that communication remains ineffective. This is significant because a larger reputational injury can strengthen the case for credibility-diluting laxity. It connects to Proposition 4, threshold harm, second-best policy, ineffective communication, credibility dilution, and bounded remedies.

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Naïve and Bayesian models make opposite recommendations under binding caps and large defamation harms

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 18–20, that a naïve audience believes every disparaging statement regardless of how common false speech becomes. For it, raising capped damages always reduces false attacks and the maximum award is optimal. A Bayesian audience discounts accusations under very lax law but trusts some false claims under partially effective law; when the resulting harm is large, the optimal award can instead be low enough to preserve skepticism. This is significant because audience assumptions reverse comparative statics and policy choice. It connects to naïve belief, Bayesian belief, maximum damages, binding caps, normative reversal, and model specification.

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Moderate damages can create private returns to investing in quality that disappear under extreme regimes

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 22–23, that targets may invest in safety, hygiene, product quality, or other traits that increase the chance of becoming a good type. Under extreme regimes, audiences ignore speech and interact on priors, so becoming better yields no informationally mediated private return. Moderate damages widen the payoff gap between good and bad types and can encourage socially valuable quality investment. This is significant because information law shapes production incentives before any statement occurs. It connects to endogenous quality, dynamic efficiency, information asymmetry, investment incentives, market discipline, and moderate regulation.

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Adding truth speakers and speakers biased toward praise makes positive and negative messages imperfect mixtures rather than pure signals

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 23–24, that realistic speaker populations include disparagers who benefit from avoidance, truth speakers who value accurate expression, and eulogists who favor interaction and may praise bad targets. Negative speech then mixes truth and strategic attack, while nonnegative speech mixes truth and strategic praise. Audiences infer target quality from the relative proportions of these speaker types. This is significant because credibility depends on population composition as well as legal price. It connects to honest speakers, eulogists, strategic bias, mixture signals, false praise, and speaker heterogeneity.

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With truth speakers present, lax law can preserve some information, whereas extremely strict law still makes all negative speech uninformative by eliminating it

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 24–25, that zero or very low damages need not reduce every message to noise once some speakers value truth. A negative statement remains probabilistically informative because it may come from a truth speaker, and praise remains imperfect because eulogists may praise bad targets. Extremely high damages are worse: they deter negative statements from truth speakers and disparagers alike, forcing the audience back to priors. This is significant because speaker diversity can make laxity informationally superior to strictness. It connects to truth speakers, cheap talk, probabilistic signals, eulogists, extreme sanctions, and prior beliefs.

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Moderate damages remain optimal with heterogeneous speaker motives even though eulogists prevent complete type revelation

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 24–25, that raising damages to a moderate level selectively deters disparagers from lying about good targets while leaving truth speakers’ accurate warnings. A suitable award can make every negative statement truthfully identify a bad target and avoid litigation, although positive silence or praise remains imperfect because eulogists may protect bad targets. The resulting equilibrium maximizes feasible information and interactions. This is significant because the superiority of moderation survives a major realism extension. It connects to robust comparative statics, heterogeneous motives, selective deterrence, imperfect revelation, moderate damages, and optimal communication.

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A committed public enforcer can sustain some informative speech with low damages because speakers face a lawsuit risk even when private targets would not sue

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 25–26, that a public agency may commit ex ante to sue with a stated probability even when litigation would not pay ex post. That commitment deters some false speakers at damages too low to motivate private plaintiffs, leaving negative and nonnegative statements partially informative when the audience threshold is near its prior. This is significant because commitment power can substitute for damages in preserving credibility. It connects to public enforcement, ex ante commitment, private enforcement, low damages, agency litigation, and credible threats.

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Public enforcement cannot achieve complete separation because the agency lacks the target’s private information and litigates probabilistically across types

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 26–27, that a public enforcer’s commitment is also a handicap. Because the agency does not observe whether the target is good or bad, any nonprohibitive damages regime leaves some good targets disparaged, some bad targets undescribed, or both. Full revelation is unavailable, and commitment generates actual litigation costs. This is significant because enforcement capacity without private information can reduce screening precision. It connects to public agencies, informational disadvantage, type screening, incomplete revelation, enforcement cost, and probabilistic suit.

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Private enforcement can dominate public enforcement because informed targets self-select into suit and thereby help reveal case merit

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 27, that private enforcement delegates litigation to the person who knows whether the accusation is false. Moderate damages can induce good targets to sue and bad targets to abstain, and speakers anticipate that separation. A public agency that lacks target type cannot reproduce the same informative screening. This is significant because decentralized enforcement creates information through plaintiff selection, not merely deterrence. It connects to private information, plaintiff self-selection, decentralized enforcement, screening, case merit, and institutional design.

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Sufficiently inaccurate courts can eliminate the separating range and make very low damages optimal even without a formal cap

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 27–28, that large judicial error can invert the critical thresholds: bad targets become willing to bring frivolous suits before damages are high enough to deter false attacks on good targets. No award then simultaneously preserves truthful warnings and eliminates lies. Because partially credible speech necessarily includes false accusations, the same logic as a binding cap can make deliberately ineffective, very-low damages optimal. This is significant because adjudicative accuracy acts as an endogenous ceiling on useful enforcement. It connects to inaccurate courts, threshold inversion, separating equilibrium, wrongful liability, second-best damages, and institutional quality.

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Defamatory harm requires credible speech, and credibility is partly produced by the consequences law attaches to false statements

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 28, that a speaker cannot harm a target merely by wishing to do so; an audience must find the derogatory statement credible and change behavior. Defamation law alters expected consequences for speaking and suing, thereby changing which statements appear and what the audience infers from them. Modeling belief formation is therefore necessary to evaluate regulation. This is significant because law partly creates the potency of the speech it regulates. It connects to credibility production, behavioral harm, belief formation, legal signals, audience action, and endogenous effects.

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When accurate adjudication and large feasible damages are unavailable, defamation regulation can cause more harm than benefit

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 28, that accurate courts plus sufficiently large feasible damages can largely eliminate false speech, but weaker institutions may not. In constrained settings, partially effective law can lend credibility to remaining lies and generate substantial litigation costs; in other parameter ranges, its improved information can still justify regulation. The outcome depends in part on the harm from blocked good interactions. This is significant because institutional limits make the policy answer contingent rather than monotonic. It connects to second-best regulation, court accuracy, feasible damages, litigation costs, false credibility, and parameter dependence.

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The framework is a starting point for heterogeneous audiences, imperfectly informed speakers, and truth-motivated plaintiffs

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 28–29, that several omitted behaviors may widen the gap between naïve and Bayesian predictions. Some plaintiffs sue to vindicate truth rather than maximize money, and large awards might crowd out that intrinsic signal; audiences may differ; and speakers may possess noisy rather than perfect information about the target. These are extensions for future research rather than resolved results. This is significant because the baseline’s clean policy conclusions depend on deliberately narrow behavioral assumptions. It connects to intrinsic motivation, signaling motives, heterogeneous audiences, noisy information, future research, and model boundaries.

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The formal equilibrium conditions require audience optimality, target litigation optimality, speaker optimality, and Bayesian consistency of beliefs

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on pages 29–31, that a Perfect Bayesian equilibrium in their game must satisfy four linked conditions. The audience interacts only when its posterior exceeds a threshold; each target sues only when expected recovery exceeds cost; the speaker selects the payoff-maximizing message in anticipation; and on-path audience beliefs follow Bayes’ rule from the speaker strategy. These conditions discipline the comparative statics rather than leaving credibility assumed. This is significant because every behavioral claim must be mutually consistent across all three actors. It connects to sequential rationality, Bayesian consistency, posterior thresholds, best responses, litigation choice, and equilibrium proof.

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The audience cannot rationally adopt an equilibrium rule that systematically inverts the meaning of disparaging and non-disparaging statements

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 31, that an effective equilibrium must have the audience respond to disparagement by avoiding and to nondisparagement by interacting. An inverted rule would cause speakers to choose nondisparagement, which returns the audience’s on-path belief to the favorable prior and contradicts avoidance. The appendix also rules out unconditional avoidance under the maintained prior. This is significant because the model’s informative equilibria preserve the intuitive direction of the signal. It connects to Proposition 2, equilibrium contradiction, signal direction, on-path beliefs, audience rationality, and Bayes’ rule.

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At both damages extremes, Bayesian consistency forces audiences back to their prior regardless of any proposed message-responsive strategy

Professors Yonathan Arbel and Murat Mungan claim, in “Defamation with Bayesian Audiences” on page 31, that the formal proof of Proposition 2 closes possible escape routes from the extremes result. With damages below the suit threshold, no target litigates and every motivated speaker disparages, so the negative-message posterior equals the prior. With damages above the deterrence threshold, every target sues and every speaker stays silent, so the nonnegative-message posterior equals the prior. This is significant because ineffective communication follows from equilibrium consistency, not a verbal assumption. It connects to extreme damages, posterior collapse, pooling strategies, litigation threshold, deterrence threshold, and formal robustness.

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