Yonathan A. Arbel & Murat C. Mungan, Defamation with Bayesian Audiences, 52 J. Legal Stud. 445 (2023).

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.

The audience channel is the paper’s central correction to conventional deterrence-and-compensation analysis.

Bayesian updating
credibility
audience effects
defamation damages
cheap talk
third-party behavior

The model uses a representative rational audience and does not claim that all real audiences update identically or without bias.

The abstract and introduction explain that legal strictness changes audience beliefs and their propensity to act on speech.


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.

The three-feature architecture isolates why standard models overstate the case for ever-higher sanctions.

Bayesian games
Type I error
Type II error
judgment-proof defendants
constitutional damages limits
litigation incentives

The baseline model simplifies parties, types, audiences, and remedies to make the joint mechanisms analytically tractable.

Pages 2–3 list the Bayesian audience, court errors, and damage cap and summarize the three-party sequence.


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.

The separating equilibrium supplies the benchmark against which lax, strict, and capped regimes are evaluated.

separating equilibrium
truthful revelation
deterrence
beneficial interaction
harmful interaction
optimal damages

Complete separation requires sufficiently accurate courts and feasible damages in the model’s intermediate range.

Page 2 identifies the first main result: a damages level that deters false speech while preserving honest information.


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.

The curve rejects the presumption that either maximum speaker freedom or maximum plaintiff protection is always best.

Laffer curves
cheap talk
chilling effects
frivolous claims
inverse-U welfare
information loss

The precise thresholds and shape depend on model parameters and the existence of effective communication equilibria.

Page 2 states the second main finding and contrasts low-cost cheap talk with high-cost overpriced talk.


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.

The damage-cap result is the defamation-specific contribution that most sharply departs from naïve-audience models.

bounded damages
credibility effects
false negatives
prior beliefs
litigation costs
counterintuitive regulation

The result arises when the cap binds below the fully revealing range and depends on the relative values of good and bad interactions.

Pages 3–4 explain why capped strictness can create misplaced trust and why laxity may dominate when defamation harms are large.


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.

The mechanism identifies institutional fallibility as the central cost of the strongest uncapped regime.

wrongful liability
frivolous litigation
judicial accuracy
excessive damages
truthful criticism
error costs

The baseline assumes errors are relatively infrequent; a later extension considers larger error rates.

Pages 3–4 contrast error-free courts, where large damages only deter lies, with error-prone courts, where they chill truth.


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.

The distinction explains why models without belief formation systematically favor stricter capped remedies.

naïve audiences
Bayesian skepticism
stigma dilution
equilibrium beliefs
reputational harm
endogenous credibility

Dilution can also make true warnings less effective; the result concerns the tradeoff, not an unqualified benefit from more false speech.

Pages 3–4 contrast fixed audience harm in prior work with Bayesian discounting when weak law makes false allegations common.


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.

The broader applicability turns a defamation model into a framework for third-party response to regulated information.

securities disclosure
false advertising
whistleblowers
crime reporting
information law
credibility design

The paper focuses formally on defamation and only comments on how domain-specific institutions might alter other applications.

Page 4 identifies several false-speech regimes sharing the sanctions-versus-informativeness tension.


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.

The literature synthesis locates the model at the intersection of defamation economics and strategic communication.

Posner
signaling theory
Crawford-Sobel cheap talk
informal sanctions
media incentives
law and economics

The review is selective and the formal model does not incorporate every political, journalistic, or philosophical concern in defamation scholarship.

Pages 4–6 review sparse economic work and identify Bayesian audience accounts, signaling, and cheap talk as the paper’s methodological foundation.


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.

The sequence formalizes the causal chain that two-party accounts truncate at publication or injury.

private information
target quality
representative audiences
interaction decisions
litigation sequence
Perfect Bayesian equilibrium

Targets have two types, the speaker knows type perfectly, and a homogeneous audience makes a binary interaction choice.

Pages 6–7 define the speaker, target, audience, types, statements, interaction decision, and conditional opportunity to sue.


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.

Speaker heterogeneity is the mechanism through which legal strictness changes the composition and credibility of observed speech.

heterogeneous speakers
private benefit
expected sanction
selection effects
partial deterrence
strategic disparagement

The baseline initially emphasizes disparagers; honest speakers and speakers biased toward praise enter in a later extension.

Pages 6–7 define the speaker’s private type as the benefit from blocking interaction and relate it to the expected litigation price.


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.

The dual response of targets and speakers explains why damages can improve information in one range and destroy it in another.

expected damages
judicial error
plaintiff selection
speaker deterrence
litigation costs
remedy design

Trial probabilities are treated as exogenous and courts are assumed committed to merits review rather than updating from case selection.

Pages 7–8 define damages, litigation cost, type-dependent plaintiff victory, and the players’ expected payoffs.


Effective and Ineffective Communication Equilibria

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.

The definition separates regimes that merely possess equilibria from regimes capable of changing informed conduct.

Perfect Bayesian equilibrium
informative communication
audience action
pooling
prior beliefs
equilibrium refinement

The definition calls communication effective if it changes avoidance with any positive probability; it does not require complete truth revelation.

Page 9 defines effective communication by the audience’s positive probability of avoiding based on received information.


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.

Proposition 1 creates an equilibrium-selection boundary around every later welfare comparison.

multiple equilibria
self-confirming beliefs
pooling
priors
equilibrium selection
legal irrelevance

The proposition establishes existence, not that ineffective equilibria will be selected or persist empirically under every regime.

Page 9 states and proves that ineffective communication equilibria exist under all defamation regimes.


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.

The result formally establishes the nonmonotonic relationship between sanction size and communication.

Proposition 2
cheap talk
overpriced talk
litigation thresholds
moderate damages
information transmission

The existence and boundaries of the effective range depend on court accuracy, costs, audience thresholds, and speaker-type distribution.

Pages 9–10 state Proposition 2 and explain why both extremes leave audiences acting on priors.


Moderate Damages and Effective Communication Equilibria

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.

The mechanism produces the upward-sloping segment of the paper’s welfare curve.

lower-moderate damages
meritorious suits
selective deterrence
false disparagement
litigation reduction
audience belief

Effective communication in the lowest part of this range may not be supportable if remaining false statements are too frequent for the audience to trust.

Pages 10–12 define critical damages and show that increasing lower-moderate damages reduces disparagement of good targets.


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.

The intermediate range achieves the paper’s first-best informative benchmark.

full separation
truthful warning
frivolous-suit deterrence
target type
perfect information
private enforcement

The result requires damages to fall between type-specific thresholds and assumes sufficiently accurate adjudication.

Page 12 derives beliefs of one and zero and identifies all effective equilibria in the intermediate range as separating.


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.

The mechanism produces the downward-sloping segment of the welfare curve and distinguishes reduced litigation from improved policy.

upper-moderate damages
frivolous suits
truthful-speech chill
bad interactions
wrongful liability
selection effects

The model assumes bad targets may sue when expected awards exceed costs and abstracts from sanctions for frivolous litigation.

Pages 12–13 show how high damages induce bad-target suits and reduce the probability of truthful disparagement.


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.

The welfare derivation integrates the behavioral mechanisms into the paper’s formal Laffer-curve result.

social welfare
inverse-U curve
separating equilibrium
litigation cost
interaction surplus
nonmonotonic regulation

The welfare function sums modeled payoffs and omits values such as autonomy, democratic speech, distribution, and error aversion not represented in the game.

Pages 14–16 derive welfare in each damages range and explain why its slopes are positive, flat, and negative.


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.

The proposition states the model’s strongest positive recommendation before legal and wealth constraints are introduced.

Proposition 3
first-best welfare
complete revelation
interaction matching
intermediate damages
feasibility

The recommendation depends on feasibility and baseline accuracy; caps or substantial judicial errors can eliminate the separating range.

Page 16 states Proposition 3 and explains why full type revelation produces greater welfare than any other modeled equilibrium.


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.

The feasibility constraint creates the setting in which the Bayesian and naïve policy prescriptions sharply diverge.

judgment-proof speakers
constitutional due process
damage caps
constrained optimization
feasible remedies
incomplete deterrence

The paper treats the upper bound as exogenous and does not separately model insurance, settlement, or asset shielding.

Pages 16–17 introduce an upper bound below the separating threshold and reduce the feasible choices to ineffective or partially effective regimes.


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.

The tradeoff makes the harm from defaming good targets the decisive parameter in the bounded regime.

classification error
beneficial transactions
harmful transactions
Bayesian priors
partial revelation
welfare tradeoffs

The baseline assumes the prior favors interaction and treats good and bad interaction payoffs in a stylized binary form.

Pages 17–18 compare universal interaction under ineffective speech with the mix of correctly and incorrectly blocked interactions under capped effective speech.


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.

The result reverses the intuition that greater plaintiff harm necessarily calls for the strictest feasible law.

Proposition 4
threshold harm
second-best policy
ineffective communication
credibility dilution
bounded remedies

The proposition is conditional on a binding cap and the model’s payoff structure; it is not a categorical recommendation to abolish defamation law.

Pages 17–18 state and explain the threshold at which ineffective communication yields at least as much welfare as every feasible effective equilibrium.


Welfare with Bayesian Versus Naïve Audiences

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.

The comparison shows that treating audiences as passive is not a harmless simplification in the constrained setting.

naïve belief
Bayesian belief
maximum damages
binding caps
normative reversal
model specification

The paper compares two stylized audience types; real audiences may update imperfectly and heterogeneously between those poles.

Pages 18–20 derive the naïve-audience behavior and contrast its maximum-damages prescription with Bayesian low-damages optimality.


Endogenous Types and Dynamic Efficiencies

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.

The extension adds long-run quality effects to the baseline’s static interaction and litigation welfare.

endogenous quality
dynamic efficiency
information asymmetry
investment incentives
market discipline
moderate regulation

Whether the induced investment is socially beneficial depends on its cost and spillovers, and the paper models that stage only schematically.

Pages 22–23 replace exogenous type with costly quality investment and show why moderate informative regimes create a payoff to becoming good.


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.

The extension tests whether the main result survives motives that run both with and against the baseline disparager.

honest speakers
eulogists
strategic bias
mixture signals
false praise
speaker heterogeneity

The law’s asymmetric treatment of false positive statements is acknowledged but left outside the article’s scope.

Pages 23–24 define three speaker types and derive audience beliefs from the ratios of truth speakers, disparagers, and eulogists.


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.

The result strengthens the paper’s rejection of extreme damages under more realistic heterogeneous motives.

truth speakers
cheap talk
probabilistic signals
eulogists
extreme sanctions
prior beliefs

Lax communication is effective only when audience thresholds fall between the message-conditioned beliefs generated by the population mix.

Pages 24–25 show that low-law messages retain some type information with truth speakers, while high law suppresses all negative signals.


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.

The extension distinguishes robustness of the policy ranking from loss of the baseline’s perfect positive signal.

robust comparative statics
heterogeneous motives
selective deterrence
imperfect revelation
moderate damages
optimal communication

The equilibrium is only imperfectly informative when false praise remains, and its support still depends on audience response thresholds.

Pages 24–25 show that moderate damages deter false negative speech, preserve honest warnings, and yield optimal imperfect information despite eulogists.


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.

The public-enforcement extension shows an informational advantage of institutional commitment unavailable to ordinary targets.

public enforcement
ex ante commitment
private enforcement
low damages
agency litigation
credible threats

The result requires an observable commitment probability and an audience whose interaction threshold is not too far from its prior.

Pages 25–26 replace the target’s suit choice with a committed agency probability and show why low damages can still deter some speakers.


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.

The claim identifies the fundamental tradeoff between public commitment and private access to case merit.

public agencies
informational disadvantage
type screening
incomplete revelation
enforcement cost
probabilistic suit

The comparison abstracts from public agencies’ possible advantages in investigation, evidence production, scale, and access to reports.

Pages 26–27 derive public-enforcement thresholds and explain why either good or bad types remain imperfectly signaled.


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.

The result supplies an informational rationale for defamation’s reliance on private lawsuits.

private information
plaintiff self-selection
decentralized enforcement
screening
case merit
institutional design

The modeled dominance excludes capture, differential litigation costs, investigative resources, evidence production, and other public-choice considerations.

Page 27 explicitly attributes private enforcement’s welfare advantage to the target’s superior information and type-revealing willingness to sue.


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.

The extension generalizes the lax-law result from formal remedy constraints to sufficiently poor adjudication.

inaccurate courts
threshold inversion
separating equilibrium
wrongful liability
second-best damages
institutional quality

The detailed proof appears in an earlier version, and the result is conditional on error rates and payoff parameters.

Pages 27–28 explain that high error prevents any damages amount from deterring lies without inducing frivolous suits and can favor very low awards.


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.

The conclusion restates the paper’s general causal thesis in terms directly applicable to legal design.

credibility production
behavioral harm
belief formation
legal signals
audience action
endogenous effects

Credibility also depends on evidence, source identity, media systems, and psychology that the formal model does not represent.

Page 28 explains that harm requires belief and that legal consequences determine the credibility of negative statements.


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.

The conclusion resists universal prescriptions and ties optimal strictness to attainable enforcement quality.

second-best regulation
court accuracy
feasible damages
litigation costs
false credibility
parameter dependence

The model identifies conditions and mechanisms rather than estimating which regime or parameters describe a particular jurisdiction.

Page 28 contrasts the accurate, unconstrained first best with settings where credibility and litigation costs can make enforcement harmful.


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.

The limitations specify where empirical and theoretical refinement is most likely to change the model.

intrinsic motivation
signaling motives
heterogeneous audiences
noisy information
future research
model boundaries

The paper does not solve these extensions and therefore does not claim robustness to all plaintiff, audience, or speaker heterogeneity.

Pages 28–29 list truth-motivated litigation, motivational crowd-out, heterogeneous audiences, and imperfect speaker knowledge as omitted possibilities.


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.

The appendix makes explicit the formal foundation beneath the article’s intuitive policy results.

sequential rationality
Bayesian consistency
posterior thresholds
best responses
litigation choice
equilibrium proof

Off-path beliefs remain partly unrestricted where a message is never sent, as is standard in Perfect Bayesian equilibrium analysis.

Pages 29–31 define the game tree and enumerate four requirements governing audience, target, speaker, and beliefs.


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.

The proof excludes perverse equilibria in which negative speech is interpreted as evidence of goodness.

Proposition 2
equilibrium contradiction
signal direction
on-path beliefs
audience rationality
Bayes’ rule

The proof depends on the maintained assumption that absent additional information the audience prefers interaction.

Page 31 proves part of Proposition 2 by showing that inverted or unconditional avoidance strategies contradict Bayesian beliefs and best responses.


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.

The proof anchors the Laffer-curve intuition in the model’s full equilibrium requirements.

extreme damages
posterior collapse
pooling strategies
litigation threshold
deterrence threshold
formal robustness

The result belongs to the baseline game; the truth-speaker extension qualifies the low-damages side while preserving the high-damages conclusion.

Page 31 derives prior beliefs from universal disparagement at very low damages and universal silence at very high damages.