# Regulating Information With Bayesian Audiences Canonical page: https://works.battleoftheforms.com/papers/ssrn-3452662/ J,V0N0 1 Regulating Information With Bayesian Audiences YonathanA.Arbel1andMuratMungan2 1SchoolofLaw,UniversityofAlabama 2ScaliaSchoolofLaw,GeorgeMasonUniversity We analyze the regulation of false statements in the presence of Bayesian audiences. We find that: (a) Often, moderate sanctions are optimal even though strict sanctions can fully deter all false statements; (b) the existence of separating equilibria—where only truthful statements are made—critically depends on judicial accuracy; (c) the magnitude of sanctions trades-off false information, chilling of truthful statements, and litigation costs; and (d) private enforcement often dominates public enforcement despite the lack of commitment. We emphasize the case of defamation law, and discuss other contexts including securities regulation, whistle-blower incentives, jury trials, andreportsofcriminalactivity. WearethankfulforthecommentsofScottBaker,AlbertChoi,EzraFriedman,NunoGaroupa,AlexLee,BenMcMichael,AlanMiller,SepehrShahshahani, Kathy Spier, Bruno Srulovici, Abe Wickelgren, and the participants of the2019LawandEconomicTheoryConference. 1. Introduction In many contexts, we use the law to regulate the exchange of information betweenprivateparties.Acommonconcernisthataninterestedspeakerwould spreadfalseinformationtoadvanceitsownprivategoals.Topreventthis,the lawwillsometimespunishfalsestatementsorrewardtruthfulones. A common neglect in the literature is the interaction between the severity of the law and the audience’s beliefs and actions. In reality, audiences processinformationdifferentlywhenitsveracityisstrictlyregulated.Thisneglect maybeduetothenaturaltendencytofocusonthepartiesthattakeanactive partinthelegalprocess(thevictim-defendantandthespeaker-plaintiff)andto abstractfromnon-participatingparties,namelythepublic(Heymann, 2012). Whateverthereason,regulationoftheinformationenvironment—theflowand qualityofinformationtothepublic—affectsaudiencesandtheirbeliefsquite directly. Ourobjecthereistobridgetheaudiencegapbyformalizingtheinteraction betweenspeakers,thetargetsoftheirspeech,andmembersoftheaudience.We employatoolthatisnaturallyaptatanalyzingthisissue,namely,aBayesian game,andweinvestigatetheimpactofthestrictnessofthelawontheemergingPerfectBayesianEquilibria(PBE).Underthisframework,aspeaker,who has private information about a business or individual (“target”), may make Draft,Vol.0,No.0, doi:/ewmxxx (cid:13)c . Allrightsreserved.ForPermissions,pleaseemail: 2 .V0N0 claims about the target to an audience member. The audience member then decideswhethertointeract—trade,trust,socialize—withthetarget.Ifthetarget loses an interaction, he may bring a lawsuit against the speaker. Within thisframework,itissociallyoptimalforaudiencestoonlyinteractwithhighquality targets and avoid low-quality ones. The key variable of interest is the strictness of the law, which we operationalize through the level of damages awarded to the target if the lawsuit is successful—this reflects the relatively broaddiscretioncourtshaveinthedeterminationofdamages(Steenson2014). Our model contains four key features: (i) The information is provided by aparty(thespeaker)whoisinterestedininfluencingtheaudience’sbehavior, (ii)theaudiencemakesdecisionsinlightofthecontentofthesuppliedinformation,(iii)thespeaker’sobjectiveconflictswiththatofanotherparty(thetarget),and(iv)thelawpenalizesthesupplyoffalsenegativeinformationbythe speaker.Thesekeyfeaturesarepresentinmanycontexts,including: defamation law, whistle-blower rewards, complaint-driven law enforcement, and securities regulation. In some of these contexts, legal proceedings are initiated by the target (private enforcement) and in others by a governmental agency (publicenforcement).Giventhegrowingpressuretoincreasetheregulationof defamatoryspeechcomingfromtheSupremeCourt,politicalleaders,lawyers, andscholars(Arbel&Mungan, 2019),wefocusondefamationlawasourrunningexamplewithprivateenforcementinourbaselinemodel(Sections3and 4).Wesubsequentlyextendtheanalysistocomparepublicandprivateenforcement,anddiscussspecificfieldsbesidesdefamationlaw(inSection5). Our analysis reveals five central findings. First, the harmful effect of disparaging statements is deeply related to the strictness of the law itself. A speaker’sstatementsmayinformtheaudience’sbeliefsandactions.Inchoosing whether to make disparaging statements, speakers will consider the expectedcostofapotentiallawsuitagainstthem.Stricterlawsincreasethiscost. Thus, inequilibrium, thestrictnessofthelawaffectsspeakersand, anticipatingthis,alsotargetsandaudiences.Theseeffectssometimesresultincounterintuitive implications, such that targets of speech who are ‘good’ types may preferlaxerlaws,eventhoughitwouldlimittheirrecoveryinasuccessfullawsuit.Suchaconclusionispossiblebecausestrictlawsmakestatementsamore costlysignal,andthus, amorereliableoneintheeyesofaudiencemembers. Adeterminedspeakercouldabusethistrustandspreadfalsitieseffectively. The second conclusion is closely related to the dynamics which we just highlighted. We find that both very strict and lax laws have similar negative informationalconsequences.Whenthelawislax,i.e.damagesarelow,speakersfrequentlymisstatethetruthandaudiencesrelymoreontheirpriorsrather than on statements (akin to babbling equilibria under cheap talk). However, if defamation laws are very strict, i.e., expected damages are high, then this may deter speakers from making even truthful assertions (“overpriced talk”). Whereas truth is a defense to a lawsuit, the risk of judicial mistake may be -- 3 mation.1Thus,ouranalysisrevealsabasicinsightwithrespecttoregulationof the information environment: Both cheap and overpriced talk can undermine informationdissemination. Third,ouranalysisilluminatestheimportanceofinstitutionalconsiderations indesigninginformationregulatinglaws.Onekeyconsiderationisthecourt’s subject-matter expertise and likelihood of delivering accurate judgments. If, in a given area, judges can fairly accurately detect false statements, imposingrelativelylargedamagesthatdeterfalsestatementscanleadtoseparating equilibriawhereonlytruthfulstatementsaremade.Usingthelawtoregulate informationcontinuestobeoptimalincaseswherecourtsdonothavetheaccuracynecessarytoimplementseparatingequilibria,but,candetermostfalse statementswithoutchillingtruthfulstatements.Whencourtsarelesscapableof accuratelyadjudicatingstatements,thesocialcostofusingthecourtsystem— operationalizedbylitigationcosts—iskeyindeterminingwhetherinformation shouldberegulated.Eveninthesecases,whenthegainsfromfacilitatingbeneficialinteractionsanddeterringharmfulonesdwarfslitigationcosts,moderate damagesemergeastheoptimalchoice.2 Anotherimplicationpertainstothepotentialdynamicimpactofinformation regulating laws. Specifically, moderate laws that cause the audience to rationally rely on speakers’ statements broadens the gap between the frequency withwhichtheaudienceinteractswithgoodtypesversusbadtypes.Thisnaturally increases the returns from being a good versus a bad type, thereby incentivizing individuals and firms to increase the quality of their products or services. Lastly, our comparison of public and private enforcement reveals the relativemeritsofprivateenforcement.Apublicagencymaybeabletocommitin advancetoacertainlevelofenforcement.Whereasprivatepartiesarelesscapableofcommitment,theyenjoyanaturalinformationaladvantageregarding the merit of the lawsuit, as they know their own type. Consequently, private enforcement leads to more accurate litigation decisions, and an intuitive advantage of private enforcement emerges in our model: separating equilibria canonlybeachievedthroughprivateenforcement. Overall,ourframeworkandresultsaddtotheliteratureoninformationregulation by spotlighting the importance of audience effects, offering a formal framework that accounts for audiences, and emphasizing the risks of overlystringentandlaxregulatoryregimes. Thenextsectionofferssomebackgroundandreviewstherelatedliterature. Section3presentsthemodelanditsanalysiswithafocusoncaseswherethe courts are relatively accurate. Section 4 explains, in detail, the more complicated trade-offs that emerge when courts are not accurate enough to achieve separatingequilibria.Section5includesseveralpotentialextensionsoftheba1. Whenweconsiderhonestandothertypesofspeakers,wealsoshowthatstrictlawscanbe worsethanlaxones,forsimilarinformationalreasons. 2. Incidentally,thisconclusioncanofferarationaletothelongstandingdistinctionindefamationlawbetweenfactsandopinions,whicharegenerallyunregulated. 4 .V0N0 sicmodel,suchasthepublicenforcementcase,thegeneralizationofthemodel tocaseswherespeakersmaybemotivatedtospeaktruthfullyortoexcessively praisethetarget, anddiscussionsofcontextsotherthandefamationlaw.Section6providesconcludingremarks. 2. Backgroundandrelatedliterature Variouslawsregulateinformationbysanctioningfalsedisclosureorrewarding truthful sharing of information. Defamation is a classic example of the formerandwhistle-blowersofthelatter.Theliteratureonthesetopicsisdisparate, but contain the same question: How to design sanctions and rewards that would incentivize the optimal sharing of information. A common recurring omission is the possibility that the audience may update its beliefs, in a Bayesianmanner,basedonthesizeofthesanctionsorrewards.Becauseofthe fragmentednatureoftheliterature,wewillconsiderfourexamples. Defamationlawisperhapsthequintessentialexampleoftheproblemofinformationregulationandthusservesasourrunningexample.Underdefamationlaw, atargetofa(1)publicstatementthatis(2)falseand(3)harmfulto one’sreputation,cansueforallresultingdamages.Judgmentsinthisareacan resultinhighpayments, withsomecasesreportingjuryjudgmentsoftensof millions of dollars (Lesher v. Does, 2013). While courts and legislators understandthebehavioraleffectsofdefamationlaw,theyaremostlypreoccupied withtheeffectofdefamationlawonspeakers’incentives(’chillingeffect’)and victim’srights(Bar-Gill&Hamdani, 2003,Acheson&Wohlschlegel, 2018). Consequently, they share a virtually axiomatic belief that stricter defamation lawswouldbetterprotectvictims(McNamara, 2007). Until very recently, scant attention has been given to the audience effects ofdefamationlaw.Thisomissionissignificant, asdefamatoryspeechisonly harmfulifitisbothbelievedandactedupon.Thefocusofeconomicworkin thisareawasmediaoutlets,responsibleinvestigativejournalism,andpolitical corruption(Garoupa, 1999a,b,Bar-Gill&Hamdani, 2003,andDalvi&Refalo, 2007).Weamplifyhereontwoinformalcontributionsthatrecognizethe potentialimplicationsofaudienceeffects(Arbel&Mungan, 2019,Hemel& Porat, 2019)byofferingaformalandbroaderaccount. Another example of information regulation comes from the literature on whistle-blowers,whichstudiestheoptimalrewardspaidtothewhistleblower. There,aprimaryconcernisfalsereportsbythewhistle-blowerstoanenforcementagency(Givati, 2016,Buccirossietal.2017,Deoorter&DeMot, 2005). Onefindingisthatwhentheriskoffalsereportingishigh,itmightbenecessarytoavoidrewardingwhistleblowersaltogether,eventhoughthismeansloss of information. What is not accounted for is how the agency, the ”audience” of the report, reacts to information, given the size of the reward. With large rewards,theagencywouldbemorelikelytoexpectfalsereports. Lawenforcementprovidesanotherillustrativeexample.Althoughthepolice oftenhastoweighthecredibilityofacriminalactivityreport,thisrealityisnot -- 5 skyandShavell2017),whichtypicallyreliesonmodelswheretheprobability ofdetectionisonlyafunctionofenforcementexpenditures.Inreality,thepolice seeks to economize resources by investigating more thoroughly reports that appear credible—and its estimation is likely influenced by the sanctions leviedagainstthosewhofilefalsereports. A final example comes from securities regulation. There, a company selfreports its performance, under an enforcement threat by the Securities and ExchangeCommission(SEC).Theliteraturerecognizesthattheagency’senforcementcanbeanimportantcredibilitymechanism(Stulz2009),butitpays littleattentiontohowstrictenforcementinteractswithinvestorsandthetrust theyplaceincompanydisclosure. Methodologically, our article borrows tools from the rich literature on signaling(Spence1973)andcheaptalk(Crawford&Sobel, 1982).Ouranalysis canalsobeinterpretedaspartofanemergingliteraturethatlooksathowlaws canbeusedtocreateinformalsanctionsthroughthebehaviorofthirdparties (e.g.,Deffains&Fluet, 2019,Mungan2016,Be´nabou&Tirole, 2011,2006, Rasmusen1996.) 3. Model Tostudythebehavioraleffectsofinformationregulationwefocusontheexampleofdefamationlaw,forthereasonsnotedintheintroduction.Wemodel theinteractionsbetweenthreetypesofparties: thespeaker(S,she),thetarget ofthespeech(T,he),andtheaudience,capturedbyarepresentativemember (A,it).Afacesaninformationalproblem:T iseitheragoodorabadtype,and A’svalueofinteractingwithT dependsonT’stype,whichisunknowntoA. Before deciding, S, who knows T’s type, communicates with A and may eitherdisparageT ormakeanon-disparagingcomment.Asweareinterestedin defamation,weassumethatS mightbenefitfromblockinganinteractionbetweenAandT,andsoSmaychoosetodefameT–i.e.,liethatT isabadtype3. Ofcourse,manyspeakersmaybemotivatedbyadesiretospeaktruthfullyor tofacilitateinteractionsbetweenT andA,andweconsiderthispossibilityin section5.2. WemodeltheinteractionsasaBayesiangame,anduseittoidentifyPerfect Bayesian Equilibria. Figure 1, below, depicts the interactions between these threepartiesandishelpfulinfollowingthedetaileddescriptionsoftheinteractionsthatweprovide,next.4 3.1 PreliminaryNotation We consider a game where T may be one of two types t ∈ {B,G} where thelettersabbreviatebad andgood, respectively.T’stypeisprivatelyknown to himself and S, but not to A, who only knows that the proportion of good 3. Consistentlywiththelaw,truthfulnegativestatementsarenotconsidereddefamatory.However,thecourtmaymakeerrorsinascertainingwhetheranegativestatementistruthful,andthis possibilityisincorporatedinourmodel,asweexplainbelow. 4. ThefiguredoesnotdepictNature’sdrawofS’stype,duetoreasonsweexplain,below. 6 .V0N0 Figure1Extendedgametreeofthemodel. -- 7 typesisγ ∈ (0,1).5 Apreferstointeractwithgoodtypes, butnotbadtypes, because this results in a payoff of g > 0 > −b where b is the cost A bears from interacting with a bad type. On the other hand, T always prefers to interactwithAandobtainsabenefitofrfromtheinteraction.Finally,S hasan interestinwhetherAandT interactandobtainsagainofv whentheydonot interact(alternatively,v canbeinterpretedasalossincurredwhenAchooses to interact with T); v is a random variable drawn from the continuum (0,v] withthecumulativedistributionfunctionF(v).Thespecificv-drawisprivate informationavailableonlytoS,andwecallv thespeaker’stype.Weassume thatinteractionsbetweenAandT aresociallyvaluableif,andonlyif,T isa goodtype,i.e.r+g >v >0>r−b. AfterNaturedeterminesthetypesofT andS, T’stypebecomescommon knowledge among T and S (but not A). At this point, S chooses what type of statement to send A regarding T’s type. The types of possible statements follow defamation law’s distinction between disparaging statements, which are potentially actionable, and non-disparaging statements, which are nonactionable(e.g.,positiveremarks,silence,opinion,etc.).6 Subsequently, A decides on whether to interact with T or to avoid him, and, finally, T, decides whether to bring a lawsuit against S if a disparaging remarkwasfollowedbyA’schoicetoavoidinteractingwithT.Wenotethat this setting includes the possibility of T suing S, even if T is in fact a bad type,i.e.,afrivolouslawsuitmaybebrought.Thisisanimportantpossibility becausecourtsmayerrintheirjudgment.7 Tocapturetheparties’payoffs,we definethefollowing: d: damagespaidbyS toT whenthecourtfindsforT. l: totallitigationcosts.Weassumethatlitigationcostsarenotprohibitive(lx forz ∈{0,1} z (cid:98) (5) a∗(z)=1 if x l/2 fort∈{B,G} t Requirement2statesthatthePBEstrategyofT mustbesuchthatinsubgames whereS disparageshim, T litigateswheneverthecostsofdoingso(l/2)are 10 .V0N0 lower than the expected damage rewards that he can obtain from litigation. Conversely,T choosesnottolitigatewhenthecostsarehigherthanexpected damages. In the exceptional case where q d = l/2, T is indifferent between t litigatingandnot. Requirement 3 (R3): S has no profitable deviations: For all t,v pairs, s∗(t,v)maximizesplayerS’spayoff,whichcanbeexpressedas l U ≡a∗(s(t,v))(v−p∗(t)s(t,v){q d+ }) (7) S t 2 The requirement with respect to S appears more complex than the requirementsthatpertaintoT andA’sstrategies,becauseS choosesheractions in anticipation of the other players’ actions. Still, the requirement is simply that,givenherowntype,T’stype,andtheanticipatedbehaviorofAandT,S mustchoosethecourseofactionthatwouldmaximizeherpayoff. Requirement4(R4):A’sbeliefsareconsistent: x∗ =Γ(t=G|z,s∗)wheneverΓ(t=G|z,s∗)(cid:54)=Υforbothz ∈{0,1} (8) z Requirement 4 simply states that A’s beliefs must be consistent with the implied conditional probability of T being a particular type based on the equilibriumstrategyofS.Thisrequirementisapplicableonlytostrategieswhich haveapositiveprobabilityofbeingplayedbyS. Ouranalysisrevealsthattherearetwotypesofassessmentswhichsatisfyrequirements1-4,i.e.twotypesofequilibrium.One,inwhichthespeaker’sstatementshavenobearingontheaudience’sbehavior,inthesensethattheydonot causetheaudiencetochangetheirbehaviorrelativetowhattheywouldhave doneiftheyreliedonlyontheirpriors.Becausethespeaker’sstatementhasno effectonaudience’sbehavior,wetermthesePBEIneffectiveCommunication Equilibria. By contrast, when statements may affect behavior, the resulting PBE are dubbed Effective Communication Equilibria. To avoid any ambiguities in our usage of these terms, we define these two types of equilibria, as follows. Definition 1: A PBE is an effective communication equilibrium if, and only if,thereexistsz ∈{0,1}suchthata∗(z)= xˆ−min{γ,xˆ} andµ∗(s∗)(cid:54)=1−z. xˆ−γ In classifying equilibria, we use these new definitions, instead of concepts like babbling equilibria and informative equilibria, because, although these concepts are related to our defined categories, they differ from each other in meaningfulways.Specifically,althoughallbabblingequilibriaareineffective communication equilibria, the converse is not true. This can be seen by noting that, in some equilibria, S can play type-dependent strategies which do not impact the behavior of A. These equilibria would not fit the definition of babblingequilibria,butwouldnotcauseachangeinA’sbehaviorcomparedto babblingequilibria.Sinceweareinterestedinclassifyingequilibriabasedon -- 11 behavior,werelyonourbehavior-baseddefinitionofeffectivecommunication equilibria. 3.4 ImpactofDefamationLawsonEquilibriumBehavior ByusingRequirements1-4weidentifyandinterpretthePBEobtainedwith different damages, through the help of four propositions, below. Our observations can be briefly summarized as follows. Proposition 1 shows that, regardlessofthelevelofdamages, therearealwaysineffectivecommunication equilibria where A acts according to its priors, i.e., where A essentially ignoresthecontentofSsstatement.Intheseequilibria,partiescannoteffectively communicateprivateinformation.Infact.whendefamationlawsareextreme, i.e. either too lax or too strict, ineffective communication equilibria are the onlyPBEofthegame, aswenoteviaProposition2.Onlymoderatedefamationlawscanengendereffectivecommunicationequilibria.Then,wequestion whethereffectivecommunicationequilibriaaresociallypreferabletoineffectiveones.Theanswertothisquestionissurprisinglyambiguousanddepends in part on the accuracy of the courts. Proposition 3 shows that when courts are sufficiently accurate, it is possible to set damages moderately such that defamatorystatementsarefullydeterred,withoutinvitingfrivolouslitigation. Thus, separating equilibria are obtainable, and they are socially preferable to anyotherequilibria.Proposition3alsonotesthatevencourtswhicharefairly accurate, but not accurate enough to facilitate separating equilibria, can enhancewelfarethroughmoderatedamagesthroughsemi-separatingequilibria. Finally, Proposition 4 reveals that when the value of A’s returns from interactionsdwarfsotherconsiderations,PBEassociatedwitheffectivedefamation lawsarealwayssociallypreferable. Proposition 1. (i) Under all defamation regimes, there exists ineffective communication equilibria. (ii) In these equilibria, A either always interacts (γ > x) or never interacts (γ < x) with the target, and litigation never takes (cid:98) (cid:98) place. Proof. (i)Theassessmentconsistingofx∗ =x∗ =γ, 1 0 0forallz if γ >x a∗(z)= (cid:98) ; 1forallz if γ l/2 forallt∈{B,G} t 1-4,andthusconstitutesaPBEwhereAactsbasedonitspriors. (ii)Bydefinition,inineffectivecommunicationequilibriaAactsaccordingto itspriors, and, thusitalwaysinteractsifγ > xandneverinteractsifγ < x. (cid:98) (cid:98) In the former case, litigation never takes place as there is always interaction. In the latter case, if a∗(0) = 1, S could profitably deviate from her strategy byneverdefamingsincethiswouldsaveherlitigationcosts.Thus,itmustbe thecasethata∗(0) = 0,whichispossibleonlyifµ(s∗) = 1since,bydefinition,interactionnevertakesplace.ButthenS canprofitablydeviatefromher 12 .V0N0 strategy s∗ by choosing not to defame whenever t = G and v < q d+ l. G 2 Thus,litigationcannotbetakingplaceinanineffectivecommunicationequilibrium. Proposition 1 reveals that it is always possible in equilibrium for the audiencetoactaccordingtoitspriors.GiventhisresponsebyA,S hasnothingto gainbydisparagingthepotentialplaintiff,becauseherstatementshavenoeffectonA’sbehavior,yetitmaycauseT toinitiatealawsuit.Thus,nolitigation canbeobservedinsuchequilibria. Next, we turn to the question of whether defamation laws can cause A to change its behavior relative to its behavior based on its priors. Because the answer to this question depends on d, the magnitude of damages, it is worth identifyingfourcriticaldamagelevelswhichplayakeyroleintheinterpretationofresults.Figure2belowdepictstheselevels. Figure2Criticallevelsofdamages Theupperlinedepictsthefirsttwolevels( l and l )whichrelatetothe 2qG 2qB potentialplaintiff’sincentives,whereasthesecondlineincludestheothertwo levels (2v−l and 2v−l) which relate to the speaker’s incentives. These levels 2qG 2qB aredepictedontwoseparatelinesbecause,absentfurtherassumptions,twoof thesevalues(namely l and 2v−l)cannotbeunambiguouslyranked.Wecan, 2qB 2qG however,notethatthecriticalvaluesthatrelatetothespeaker’sincentivesare greaterthanthecorrespondingcriticalvaluesthatrelatetothetarget’sincentives(i.e. l < 2v−l fori∈B,G),givenourassumptionthatlitigationcosts 2qi 2qi arenotprohibitivelyhigh,i.e.l 2v−l,itfollowsthatalleffectivedisparaging 2qB -- 13 statementsaredeterred.9Thus,inneithercasedostatementshaveanimpacton theaudience’sbehavior.Wedistinguishbetweentheseextremedamages(i.e., (cid:104) (cid:105) (cid:104) (cid:105) d (cid:54)∈ l ,2v−l )andmoderatedamages(i.e., d ∈ l ,2v−l .)Theabove 2qG 2qB 2qG 2qB observationshighlightthatextremedamagescanonlyleadtoineffectivecommunication PBE. A question that remains is whether moderate damages can lead to effective communication equilibria. Proposition 2 answers this questionaffirmativelyandformalizesrelatedobservations. Proposition2. (i)Extremedefamationlawsonlygenerateineffectivecommunicationequilibria.(ii)Effectivecommunicationequilibriacanbeobtained only when the audience acts consistently with the speaker’s statement, i.e. a∗(z) = z. (iii) There are moderate defamation laws which generate effectivecommunicationequilibria. Proof. SeeAppendix. Proposition2holdsthatextremedefamationlawsonlyallowforineffective communicationequilibria,and,asnotedinproposition1,theseequilibriaalso exist under moderate defamation laws. However, moderate defamation laws alsogenerateeffectivecommunicationequilibria.Thisimpliesthatswitching fromanextremedefamationlawregimetoamoderateregimecanexpandthe typesofequilibriathatmaybeobtained.Thus, itbecomesimportanttocomparethepropertiesofthetwotypesofequilibriatoascertaintheirwelfareimpacts,amongotherthings.Thiscomparisonhingesonhowaccuratethecourt isinreturningcorrectverdicts.Byaccuracy,wemeanthefollowing: Definition2(i) qG ∈(1,∞)measuresthecourts’accuracy.(ii)π ≡ 2v−1is qB l acriticallevelofcourtaccuracyusedtoevaluatethepotentialwelfareimpacts ofdefamationlaws. Wereporttherelationshipbetweenthecourt’saccuracy,asdefinedabove,and thePBEobtainable,asfollows. Proposition3. (i)SeparatingEquilibrium:Whenthecourtissufficientlyaccurate(i.e. qG (cid:62) π)therearemoderatedefamationlawsassociatedwithPBE qB where: S disparagesT if,andonlyif,heisabadtype;theaudienceactsconsistentlywiththisinformation(i.e.a∗(z) = z); andthereisnolitigation.(ii) Separating equilibria lead to greater expected welfare than all other equilibria.(iii)Whenthecourtisinsufficientlyaccurate(i.e. qG < π), allequilibria qB involve a positive likelihood with which the audience does not interact with a good type, interacts with a bad type, or both. (iv) When the court is only 9. Weintentionallyrefertothedeterrenceofeffectivedisparagingstatements,becausethere couldbeequilibriawheretheaudiencedisregardsdisparagingcommentsandinteractswithT, and,insuchinstances,disparagingcommentswouldnotbedeterredbecausetheywouldnotgive risetolitigation. 14 .V0N0 slightly inaccurate, i.e. π − qG > 0 is sufficiently small, there exist moderqB atedefamationlawswhichgenerateequilibriathatleadtogreaterwelfarethan thosegeneratedbyineffectivecommunicationequilibria. Proof. SeeAppendix Intuitively, when courts are sufficiently accurate it ought to be possible to set damages large enough to deter defamatory statements without generating frivolous lawsuits. When qG (cid:62) π, this is in fact the case, because the amqB biguousrankingbetweenthecriticaldamagelevelsdepictedinFigure2, l 2qB and 2v−l, vanishes, and it follows that 2v−l < l , as depicted in Figure 3 2qG 2qG 2qB below. Therefore, by choosing damages in between these two threshold val- (cid:16) (cid:17) ues,i.e.d∈ 2v−l, l ,onecanachievetwoimportantgoalsatonce: deter 2qG 2qB defamationaswellasfrivolouslawsuits. Figure3Criticallevelsofdamages Separating equilibria that achieve these two goals at once naturally maximizewelfare,because(1)theyleadtointeractionsonlywhentheseinteractions enhance welfare and (2) there are no litigation costs. This reasoning extends to the case where the court is only somewhat accurate through a simple continuity argument. In this case, moderate defamation laws are associated with semi-separatingequilibria,whereinanon-disparagingcommentrevealsthatT is a good type, but where good types face a very small likelihood of being disparaged.Theseequilibrialeadtoonlyslightlylowerexpectedwelfarethan separating equilibria and, thus, are associated with greater expected welfare thanineffectivecommunicationequilibria. Propositions 1-3, together, reveal that when courts perform well in distinguishinggoodandbadtypes,moderatedefamationlawscanbeusedwithrelativeeasetoenhancewelfareandtoincreasetheinformationalvalueofstatements made by speakers. In these cases, (semi-)separating equilibria lead to obviousandunambiguousimprovementscomparedtoequilibriawheretheaudienceislefttouseitspriorstomakedecisions.Inpractice,however,thereare manycaseswherethereisexpressedconcernamongjudgesandlawyersthat discoveringthetruthisdifficultandthatlitigationisfraughtwithinaccuracies. Theanalysisinthenextsectionthusfocusesonthesesituations. -- 15 4. DynamicswhenCourtsareInaccurate The previous section explained why it is impossible to obtain separating equilibriaifcourtsareinaccurate.AsnotedinProposition3,thisimpliesthat withsomepositiveprobabilityeitherinteractionswithgoodtypesaredeterred (i.e.type-1errors),interactionswithbadtypesareundeterred(type-2errors), orboth.Inthesecases,usingstricterdefamationlaws(i.e.higherd)cangenerateatrade-offbetweencostsassociatedwiththesetwotypesoferrorsandmay alsoimpactexpectedlitigationcosts.Inthissection, wedescribethesetradeoffs. We focus exclusively on moderate defamation laws and the impact of changingdoneffectivecommunicationequilibriabecause,asnotedinProposition 3, in all other cases the audience acts according to its priors and no litigation takes place. Subsequently, we identify a sufficient condition under which achieving effective communication equilibria through moderate damagescontinuestobesociallypreferabletohavingextremedefamationlaws. Toexplainthedynamicsthatemerge,wefirststartbycalculatingtheequilibriumbeliefs,i.e.x∗ andx∗ thatwouldemergeinaPBEwherea∗(z) = z, 0 1 assuming that such an equilibrium exists. We plot these beliefs in Figure 4, below,throughaspecificbutrepresentativeexample.Thehorizontalaxisrepresentsdamages, onwhichwemarkthefourcriticaldamageslevelslistedin Figure2.Thistime,however,thecourt’saccuracyislowerthanπ,sotherankingoftheintermediatecriticaldamages(i.e. l and 2v−l)istheoppositeof thatdepictedinFigure3.Inadditiontoplottin 2 g qB beliefs, 2 i q . G e.,x∗andx∗,inFig0 1 ure4wealsoplottheex-anteprobabilityofT beingdisparagedinthesePBE. Thesearelabeledδ andδ forgoodtypesandbadtypes,respectively.Next, G B we explain how these expressions are derived in the three relevant ranges of damages. (1) In the range ( l , l ), damages are too low to incentivize bad types 2qG 2qB to sue. Thus, S faces no consequences from disparaging bad types. Whereas goodtypeswillbringalawsuit,Smightstilldisparagethemifitsbenefitfrom blockinganinteractionissufficientlyhigh, i.e., v > v ≡ q d+ l.Thus, a G G 2 badtypeisdisparagedwithcertainty,i.e.δ =1,andagoodtypemayormay B not be disparaged with positive probability. From A’s perspective this means thatapersonwhoisnotdisparagedisdefinitelyagoodtype,i.e.x∗ =1,while a target who is disparaged may or may not be a good type, but is no more likelytobeagoodtypethanarandomdrawfromthepopulation,i.e.x∗ < γ. The ex-ante probability with which S draws a benefit that is higher than v G isδ = 1−F(v ),and,thus,thisistheprobabilitywithwhichagoodtype G G is disparaged. Using this expression, x∗ can be more precisely expressed as x∗ = γδG <γ. 1 γδG+1−γ (2)Intherange( l ,2v−l),damagesaresufficienttotriggerfrivoloussuits 2qB 2qG by bad types who are disparaged. The threat of a suit causes the speaker to refrainfromdisparagingevenabadtype,unlessherbenefitfromblockingan interactionissufficientlyhigh.Still,theminimumbenefitthatleadsaspeaker to disparage a bad type, v ≡ q d+ l, is lower than the minimum benefit B B 2 thatwouldmakeherdisparageagoodtype,v =q d+ l,asfrivolousclaims G G 2 16 .V0N0 Figure4. IllustrationofBeliefsandtheLikelihoodofaDisparagingStatement. Damages=d,x∗ ,x∗ arebeliefs.qG=0.8,qB =0.2,l=0.3,andF(v)=vwithsupport (0,1]. are less likely to be successful. Thus, the ex-ante probability with which S disparages a bad type, δ = 1−F(v ), is greater than the likelihood with B B which she disparages a good type, δ = 1 − F(v ). Consequently, in this G G range,x∗ = γ(1−δG) >γ >x∗ = γδG asδ <δ . 0 γ(1−δG)+(1−γ)(1−δB) 1 γδG+(1−γ)δB G B (3)Intherange(2v−l,2v−l),damagesaresufficientlyhightodeterS from 2qG 2qB disparaginggoodtypes,evenifherbenefitfromblockinginteractionsismaximal,i.e.v.Shewillonlydisparagebadtypesifherbenefitfromblockinganinteractionissufficientlyhigh.Thus,inthisrange:x∗ =0<γ < γ = x∗andδ =0<δ =1−F(v ). 1 γ+(1−γ)(1−δB) 0 G B B This brief analysis, and its depiction in Figure 4 can be used to identify someofthewelfareimplicationsofalteringthelevelofdamages.Inthelowermoderate range (i.e. ( l , l )) damages are insufficient to completely pre2qG 2qB ventdisparagingremarksagainstgoodtypes,buttheyarealsolowenoughto deter frivolous litigation by bad types, leading to their disparagement. Thus, in this range, the only impact of increasing damages is to reduce the number ofgoodtypesbeingdisparaged.Thisreductionconsequentlyreducesexpected litigation costs, and increases the likelihood of interactions with good types. Therefore,increasingdamagesinthisrangemonotonicallyenhanceswelfare, becauseinteractionswithgoodtypesaresociallydesirable,andlitigationcosts reducewelfare. Intheintermediate-moderaterange(i.e.( l ,2v−l))damagesarelargeenough 2qB 2qG toinducefrivolouslitigationbybadtypes,butnotlargeenoughtocompletely deterdisparagingremarksagainstgoodtypes.Therefore,increasingdamages -- 17 in this range generates more meaningful trade-offs by increasing the likelihoodofbeneficialinteractionsaswellasharmfulinteractions,whilereducing the likelihood of litigation. Thus, it is desirable to increase damages in this rangeonlyifthesavingsfromlowerlitigationcostsandtheincreasedvalueof beneficialinteractionsexceedthecostinvolvedwithharmfulinteractions.Absent more restrictive assumptions, one cannot unambiguously compare these benefitsandcosts, becausetheirmagnitudesdepend, inpart, onthemarginal changesinδ andδ ,whichcantakemanyformsdependingontheshapeof B G thedistributionofspeakerbenefits(i.e.F(v)). Finally,inthehigher-moderaterange(i.e.(2v−l,2v−l)),damagesarehigh 2qG 2qB enoughtodeterdisparagingcommentsagainstallgoodtypes,butarenotsufficiently high to deter disparaging remarks against bad types. An increase in damages in this range causes an increase in the expected costs from harmful interactions, but reduces litigation costs. Thus, as long as litigation costs are lowerthanthegainsfromblockingharmfulinteractions,socialwelfareisimprovedbyreducingdamagesinthisrange. This analysis reveals the complex nature of trade-offs involved when the courtisinaccurateinmakingdecisions.Thereisnogeneralreasonwhyhigher damageswouldbebetterthanlowerdamages.Courtsandpolicymakersmust account for domain-specific considerations which can tilt the balance in any givendirection. Asomewhatcounterintuitiveconclusionisthat,withinaccuratecourts,itis noteventrueingeneralthatonecanimproveuponineffectivecommunication equilibria where the audience acts upon its priors. Moving to an equilibrium wheretheaudienceactsconsistentlywiththeinformationitreceivesfromthe speakercanbehelpfulinpromotingbeneficialinteractionsordissuadingharmfulones.However,itcomesatthecostofincreasedlitigation,andmayreduce thetarget’sbenefitfromincreasedmissedinteractionsorthespeaker’sbenefit from blocking interactions. An aspect of this analysis is that higher damages inthemoderaterangesometimessacrificethewell-beingofsomegoodtypes, thus calling into question a widely-held belief among lawyers that stronger defamationlawsprotectgoodtypes(Arbel&Mungan, 2019,Hemel&Porat, 2019). Adding to these complexities is the fact that, given any damage level, d, effective communication PBE are possible only if A’s risk tolerance, xˆ, lies inbetweenx∗ andx∗,asdepictedinFigure4.Despitetheseambiguities,one 1 0 canalwaysusemoderatedamagesthatleadtoeffectivecommunicationPBE. Thus,onecanimprovetheoddsofbeneficialinteractionstakingplaceand/or harmfulinteractionsnottakingplace.Thus,iftheaudience’swell-beingisthe predominant consideration in the welfare analysis, it follows that moderate damages can always improve upon extreme damages. The next proposition formalizesthisresult. Proposition4. Thereexistmoderatedamagesleadingtoeffectivecommunicationequilibria,whichgenerategreaterwelfarethanineffectivecommunicationequilibria,aslongasgandbarelargerelativetoothercostsandbenefits. 18 .V0N0 Proof. Theexpectedpay-offoftheaudienceinanequilibriumwherea∗(z)= zforallzis U =γ(1−δ )g−(1−γ)(1−δ )b (9) A G B Ontheotherhand,0andγg−(1−γ)baretheexpectedpay-offsthattheaudiencewouldhavereceivedbyactingaccordingtoitspriors,whenγ x,respectively.InthesePBE,itfollowsthatU =γ(1−δ )g >0when (cid:98) A G d∈( l , l ),and,similarly,U =γg−(1−γ)(1−δ )b>γg−(1−γ)b 2qG 2qB A B when d ∈ (2v−l,2v−l). Thus, for any given x, the increase in the expected 2qG 2qB (cid:98) pay-offoftheaudiencestemmingfromamovefromaPBEwhereitactsaccordingtoitspriorstoonewhereitactsaccordingtotheinformationitreceives fromthespeakerislinearlyincreasinging andb,respectively.Moreover,the magnitudes of g and b only affect A’s payoff, and, hence, there exist large enoughg andbwhichcausethesePBEtogenerategreaterwelfarethanPBE wheretheaudienceactsaccordingtoitspriors. Proposition 4 reveals that when the value of interactions are large in comparison to other considerations, like litigation costs and the benefits that the speakergetsfromblockinginteractions,moderatedefamationlawscanbeused toenhancewelfare.Thisisbecause,undertheseconditions,thedominantconsiderationbecomesthemaximizationoftheaudience’spay-off,whichbenefits fromhavingeffectivecommunicationequilibria. 5. Discussion In Sections 3 and 4, we provided a model that allowed us to clearly focus ondefamationlaws’impactontheaudience’sequilibriumbeliefsandactions. Indoingso,weabstractedfrommanyissuesthatbearontheregulationofinformationinmoregeneralsettings,particularly,thepossibilityofacommitted publicenforcer,qualitybeingendogenouslychosenbythetarget,andtheexistenceofhonestandothertypesofspeakers.Hereweturnourattentiontothese issues. 5.1 EndogenousTypesandDynamicEfficiencies Inouranalysisthusfar,weassumedthatthetarget’stypetwasexogenously determinedbynaturetobeeitherGorBwithprobabilitiesγand1−γ,respectively.Onemightquestiontherealityofthisassumption,aspeoplecanmake investmentsthatwouldmakethembetterorworsetradingpartners, e.g., createhigherqualityproducts,maintainsafetystandards,orkeephigherhygiene standards. One option of incorporating quality investments into our analysis is to replace Nature’s choice of types with a preliminary stage where the target, T, makes a costly investment (c) that can increase her likelihood of becoming a good type. Formally, we may assume that γ = γ(c) with γ(cid:48) > 0 > γ(cid:48)(cid:48), limγ(cid:48)(c) = ∞, γ(0) = γ and limγ(c) = γ where1 > γ > γ > 0.Morec→0 c→∞ over,tokeepthedescriptionofthisextensionbrief,wefocusonthecasewhere -- 19 γ >x. (cid:98) Thequalityinvestmentdecisionisnowpartofalargergame.Givenanysubgameequilibrium,thebestresponseofT istomakeaninvestmenttomaximize hisexpectedpay-off,whichcanbedenotedasγ(c)m +(1−γ(c))m −c G B wherem andm refertothepay-offsheobtainsinthesub-gameequilibria. G B This observation reveals a very clear result: When the laws are extreme, (cid:104) (cid:105) i.e.d(cid:54)∈ l ,2v−l ,thetargethasnoreasontoinvestinquality.Thisfollows 2qG 2qB fromPropositions1&2,whichshowthatwithextremelaws,theaudienceacts basedonitspriorsandinteractswiththetargetifγ issufficientlyhigh.Thus, investmentshavenoprivatereturnsforthetarget. Itisonlywhenthelawsaremoderatethattargetsmayhaveanincentiveto invest in quality. This can be demonstrated by focusing on the lower bound of intermediate damages, i.e. l . In this case, in PBE with a∗(z) = z, it 2qG followsthatm =0(asallbadtypesaredisparaged)whilem =(1−δ )r B G G (because good types are disparaged with probability δ , in which case there G isalawsuitwhichpaysthetargetexpecteddamagesequaltolitigationcosts). Thus,thetarget’spay-offisγ(c)(1−δ )r−c,and,therefore,thetargetprofits G (inexpectation)frominvesting.Whetherthisissociallygoodorbad,depends, ofcourse,onwhethertherearenetsocialgainsfromsuchinvestments.Inour context, this is socially valuable as long as the expected benefits from good interactions ((1−δ )g)—which are not internalized by T—are greater than G the expected litigation costs l and the loss of benefit to S from blocking an interaction, i.e. (1 − δ )E[v|v > l]. In fact, if investments in quality are G 2 sociallyvaluable,thenincreasingdamageswithintheintermediaterangeupto l will be desirable. This is because these higher damages lead to a lower 2qB probability of disparaging remarks made against good types (as illustrated in Figure 4) and, thus, increase m , while still keeping expected payoffs from G beingabadtypeatm =0. B Thediscussionherehighlightstheimportanceofinformationregulationfor broadermarketdynamics.Theintuitionunderlyingourresultsarestraightforward.Extremelawsleadtoineffectivecommunicationequilibria.Incontrast, moderate laws create an environment with more reliable information regarding types, thus generating a greater gap between the payoffs obtainable by goodtypesversusbadtypes.This,inturn,increasesthereturnsfrombeinga goodtype,andleadstomoreinvestments.Inrealisticsettings,providingsuch additionalincentivesissociallydesirablewhenthepotentialinvestorisunderincentivized due to problems like information asymmetries. The gains from suchinvestmentsinqualityshouldbeaddedtotheotherbenefitsofmoderate lawsthatwehaveidentified. 5.2 TruthSpeakersandEulogists So far, we only considered speakers who had something to gain from severing the relationship between the audience and the target. This abstraction followstheideaofspeaker’s’bias’inthecheaptalkliterature.Inreality,however,somespeakersmaynothavesuchmotivations.Quiteimportantly,many 20 .V0N0 people, when asked their opinion, provide an honest assessment of others. Moreover,therearealsopeoplewhoaremotivatedbydoingtheexactopposite of what the speakers in our model are motivated by; namely, promoting the relationship between the target and the audience. In what follows we distinguishbetweenthefirsttype, “truthspeakers,”thelattertype, “eulogists,”and theonesweformerlydiscussedinSection3as“disparagers.”Webriefly,and informally, explain now what occurs when these kinds of speakers are incorporatedintoouranalysis. Inourdiscussion,weconceiveofthesetypesasfollows.Disparagers,aswe noted,receiveapositivevaluefromblockinganinteraction;truth-speakersare indifferent with respect to whether the parties will interact but receive some valuefromspeakingtheirmind; and,eulogistsreceiveavaluefromtherebeinganinteraction.Therefore,solongascostsofsodoingarenothigh,disparagers will badmouth the target and truth-speakers will reveal their true type. Eulogists, in contrast, would always want to praise the target, as there is no recourse under defamation law for false positive statements (the question of whythisasymmetryexistsgoesbeyondthethescopeofourarticle). Theincorporationofthesetypesofspeakershasnoimpactontheobservationthatextremelystrongdefamationlawsleavetheaudiencetoactupontheir priors. This follows, because once a critical threshold of damages is passed, disparagers as well as truth speakers are deterred from making negative remarks.Thus,extremelystrongdefamationlawscausedisparagers,truthspeakers, and eulogists alike to abstain from making negative statements, and the audiencehasnooptionbuttoactaccordingtoitspriors. The same cannot be said, however, for extremely weak defamation laws. When damages are very low, targets lack an incentive to bring suit, making talk“cheap.”Despitethat,disparagingstatementsarestillsomewhatinformative:Giventheexistenceofsometruth-speakers,thereissomeprobabilitythat any negative statement is true. Consequently, an audience that hears a negative statement evaluates its credibility based on the ratio of truth-speakers to disparagers.Thus, (inanassessmentwherea∗(z) = z)wecanformulatethe audience’sbeliefthatthetargetisagoodtype,conditionalonanegativestatementasx∗ = γ ∆ whereτ denotestheproportion oftruthspeakers, 1 ∆+(1−γ)τ and ∆ is the proportion of disparagers. On the other hand, non-disparaging remarksdonotnecessarilymeanthatT isagoodtype.Bysimilarlogic,there is some probability that any given praise is false given the existence of eulogists.Anaudiencewhichhearsapositivestatementevaluatesitsveracityasa function of the ratio of eulogists to truth-speakers. Thus, we can express the audience’sbeliefasx∗ =γ τ+ε ,whereεistheproportionofeulogists. 0 γτ+ε Using these observations it is easy to verify that, under lax laws, both disparaging and non-disparaging statements are somewhat informative of types. Inotherwords,non-disparagingstatementsaremoreindicativeofgoodtypes than no information at all (x∗ > γ), and disparaging statements are more indicativeofbadtypesthannoinformationatall,i.e.x∗ <γ.Thus,iftheau1 dience’snecessarylevelofconfidenceforinteraction,(x),iscloseenoughtoγ (cid:98) -- 21 suchthatx∗ (cid:62) x (cid:62) x∗,onecanachieveanequilibriumwhereintheaudience 0 (cid:98) 1 meaningfullyusestheinformationprovidedbyspeakers,evenwhenthereare nosanctionsforfalsestatements.If,however,x∈/ [x∗,x∗],thenlaxlawscause (cid:98) 1 0 theaudience toignore thestatement andact accordingto its priors, as inour analysisinSection3.Thus,wefocusourremainingdiscussiontocaseswhere x∗ (cid:62)x(cid:62)x∗. 0 (cid:98) 1 Incaseswheredamagesaremoderate,someoftheclaimsmadeinSection3 need to be qualified, whereas others remain intact. In particular, it is still the case that moderate damages improve the reliability of information over extremedamages.Toseethis,consider,forinstance,theimplicationsofraising damagesfromlowlevelsto l .Amongspeakers,thischangeonlyaltersthe 2qG incentives of “disparagers,” because these are the only speakers who have an interestinmakingfalsestatementsaboutgoodtypes,who,giventhislevelof damages, bring a lawsuit against them. Thus, the proportion of disparagers who make false statements is reduced, which causes x∗ to fall and x∗ to in1 0 crease,i.e.itcausesinformationsuppliedbyspeakerstobemoreinformative. This observation reveals another of our results that carries over in a modified way: when courts are sufficiently accurate, one can use damages equal to 2v−l < l todeteralldisparagersfrommakingfalsestatementsandalso 2qG 2qB guarantee that there are no lawsuits by bad type targets. In this case, it immediatelyfollowsthatx∗ = 0, suchthatadisparagingstatementisperfectly informative. Thepresenceofeulogists,however,meansthatx∗ <1.Thus,fullyseparat0 ingequilibriaarenolongerobtainable.Still,eveninthepresenceofeulogists and disparagers, semi-separating equilibria are possible. Moreover, as in the previouscase,thesesemi-separatingequilibriaareoptimal,becausetheylead to no litigation costs, cause all possible good interactions to take place, and achievemaximumdeterrenceofbadinteractions. We conclude that the introduction of honest speakers as well as what we calledeulogists—peoplewhowishtopromotethetarget—doesnotaffectthe superiorityofmoderatedamagesoverextremeformsofdamages.Whatdoes changeisperhapssomewhatcounterintuitive: strictlawsturnouttobeworse thanlaxlaws.Strictlawsleadtocompletelyuninformativespeechinequilibriumwhereaslaxlawsstillallowspeechtobesomewhatinformative,permittingeffectivecommunicationequilibria. 5.3 CommitmentandPublicEnforcement Our analysis so far focused on private enforcement of defamation laws, where the target is the one to sue. However, private parties will only bring alawsuitifitpaystodosoex-post, andthiscalculusexposesthemtostrategicbehaviorbywould-bedefamers.Incontrast,someparties,typicallypublic agencies, maybeabletocommitex-antetosue, evenifitdoesnotpaytodo soex-post.Comparingprivateandpublicenforcementcanbeusefulinunderstanding other contexts where information is regulated, and may also illuminatethereasonswhyprivateenforcementisusedindefamation. 22 .V0N0 Tohelpinthiscomparison,weconsiderasimplemodificationofouranalysis wherein instead of the target, it is a public enforcement agency that can bring suit against disparaging remarks. The agency, however, is not privy to thetarget’sprivateinformationregardinghistype,whichisbyassumptionunobservable,andsoitcannotconditionitsactiononT’stype.Theagencythus choosessomeprobability,p∈(0,1),withwhichitwillbringalawsuit.Asthe choiceofpdoesnotdependonanynewinformation,itismadeex-anteandis communicatedto,orobservedby,would-bespeakers.Thechoiceofpreplaces p∗(t) in (6). We retain all other assumptions, including the assumption that the probabilities with which the speaker will be found liable in court are q G and q , when she makes disparaging statements against good and bad types, B respectively. This simple modification allows us to calculate the the analogs of the two critical values which describe the best responses of S depicted in Figure 2. Specifically,thesetwocriticalvaluesnowbecome 2v¯−pl and 2v¯−pl.Thus,in 2pqG 2pqB effective communication equilibria, when d > 2v¯−pl, the speaker does not 2pqG make disparaging statements against good types, and refrains from making disparaging statements against bad types when d > 2v¯−pl. It can be easily 2pqB verified that each of these values is larger than their corresponding analog in theprivateenforcementcontext,i.e. 2v¯−pl > 2v¯−l fori∈{B,G}. 2pqi 2qi The commitment to bringing a lawsuit also changes the speaker’s behavior, as a lawsuit is possible even when expected damages are low. We next explainthebehaviorofthespeakerineffectivecommunicationequilibria,under three different damages ranges, and subsequently compare them with the correspondingbehaviorunderprivateenforcement. Asunderprivateenforcement,itfollowsthatwhendamagesareveryhigh, d > 2v¯−pl, all disparaging remarks are deterred. However, when damages 2pqB aremoderate,d∈(2v¯−pl,2v¯−pl),thespeakerrefrainsfromdisparaginggood 2pqG 2pqB types,butdisparagesbadtypeswheneverhervaluefromblockinginteractions issufficientlyhigh(i.e.v˜ ≡p(q d−l) 0 (The tilde sign refers to analogs of values defined in B B the private enforcement context). Thus, in the moderate range, a disparaging remark conclusively reveals to the audience that the target is a bad type; a non-disparaging comment is an informative, but inconclusive, signal that the target is a good type, i.e. x∗ = 0 < γ < x∗. When damages are low, i.e., 1 0 d< 2v¯−pl,thespeakerisnolongernecessarilydeterredfromdisparaginggood 2pqG types,andchoosestodefamethetargetifhervaluefromblockinginteractions exceedsv˜ ≡p(q d− l).Thus,itfollowsthat0<δ˜ <δ˜ ,and,therefore, G B 2 G B 0 0, δ˜ < 1, or 2pqB G B both.Thisimmediatelyimpliesthatwhencourtsareaccurate,privateenforcementdominatespubicenforcementintermsofitswelfareconsequences.The differenceinthewelfareobtainableunderthetworegimesisenhancedfurther bythefactthatunderpublicenforcement,theenforcementagency’scommitment results in some litigation whenever defamation laws are effective (i.e. 2v¯−pl >d). 2pqB Thelastpointhighlightsamoregeneralandimportantadvantageofprivate enforcement over public enforcement. Specifically,private enforcement delegates the decision to litigate to the party with the best information about the meritsofthecase.Moderatedamagescanbecraftedtoseparategoodandbad types based on their willingness to sue, and this enables the speaker’s statementstobemoreinformativeofthetarget’stype. Insum,thiscomparisonilluminatetherelativevalueofpublicversuspublic enforcement.However,asourfocushereisoncommitment,weabstractfrom otherrelevantconsiderations, suchastherelativecostsoflearningaboutdisparagingremarksorproducingevidence.Inasmuchaspublicagenciesemploy discretion, they are also susceptible to capture and other public choice problems.Theseconsiderationsshouldalsobetakenintoaccountincomparingthe relative social desirability of pubic versus private enforcement in regulating speech. 5.4 FeaturesofDefamationLaw Ouranalysistookthedomainofpotentiallydefamatorystatements—disparaging remarks—asgiven.However,theframeworkdevelopedherecouldalsobeused toshedlightonsuchdeterminations,inparticular,thefactv.opinionandperse v. pro-quod distinctions. Defamation law renders expressions of opinion non-actionable.Theanalysissuggestsarationale: itishardertodeterminethe truth-valueofopinions,leadingtogreaterjudicialinaccuracyandmakingregulationlessvaluable.Itisalsopossiblethatthelawimplicitlyrecognizesthat 24 .V0N0 audiences are Bayesian, so that they inherently discount statements couched in the form of an opinion. The other distinction involves regular defamatory statements (pro-quod), and a category of per-se statements, which requires a lower burden of proof. Per-se statements are allegations of criminal activity, sexualmisconduct,contagiousdisease,orimproperbusinessdealings.Again, our analysis offers a rationale: In such cases, the harm to the target and the gain to the speaker may be especially high. Consequently, stricter protection maybewarranted. 5.5 InformationRegulationinOtherSettings Aswenotedintheintroduction,themodelpresentedinsections2and3has keyfeatureswhicharepresentinmanycontexts, andwefocusedondefamationlawduetoitscurrentimportance.Herewediscussthreeotherimportant settingswherethesekeyfeaturesarepresent: lawenforcement,jurytrials,and whistle-blowers.Thenwediscussanadditionalcontext,securitiesregulation, wherethespeakerrevealsinformationaboutitself.Despitethisconceptualdifference,thecurrentframeworkprovesilluminatinginconsideringtheoptimal regulatoryframework. 5.5.1 BayesianPublicEnforcers Newsaboutcrimeswhichwerecommitted after the police chose to ignore reports of abuse and other red flags are, unfortunately, not uncommon.10 At the same time, some people make false or frivolousreportsaboutothers.11 Policeforceshavelimitedresources, sothey needtoprioritizethecallstheyreceiveandfocusonthosetheyperceivetobe mostcredible. Onecanconceiveofthisdynamicassimilartotheonepresentedhere.Law enforcerswhoreceivereportshavetoweighthecredibilityandtheimportance ofeachclaim.Theydecidetotakeactiononlywhenitsexpectedbenefitsare sufficientlylargegivenenforcementcosts.Assuch,enforcersactastheaudience. The person reporting the crime is akin to the speaker, and the alleged criminalisthetarget. Inthiscontext,punishingfalsereportshastheeffectofmakingreportsmore credible, as in our analysis, and allowing law enforcers to more accurately focustheirenforcementefforts.This,inturnhastheeffectofincreasingdeterrenceby increasingthe opportunitycostto committingcrime(i.e. theanalog of reducing δ ). However, if false reports are punished too severely, it will G have the effect of deterring truthful reports and, thus, lead to less than ideal deterrenceoftheunderlyingcrime. 10. EmmaSnaith, Womankilledbyex-boyfriendafterpolicewerewarned18timesofhis abuse,Independent(Aug.,16th,2019).JoelRose&BrakktonBooker,ParklandShootingSuspect: AStoryOfRedFlags,Ignored,NPRNews(March,12018) 11. Swatting, e.g., is a practice of fraudulently reporting a bomb or other imminent threat comingfromthevictiminordertohavepoliceforcesstormtheirresidence,sometimestotragic ends -- 25 5.5.2 Whistle-blowing Asimilardilemmaappliestowhistleblowers.TheUS government sometimes issues rewards to whistleblowers (e.g., False Claims Act and the IRS Whistleblower Law) in order to encourage them to report wrongdoing despite their fears of retribution and informal sanctions (Givati, 2016). The concern is that rewards may incentivize false whistle-blowing among people who face low costs and may also fail to appropriately incentivize people with abnormally high costs. In analyzing this problem, one can think of whistleblowers as speakers and law enforcement agencies as the audience.Theagencydilemmaishowtosetrewardsandpenaltiesinawaythat would allow for the effective transmission of private information without involvingtoohighverificationandlitigationcosts. 5.5.3 Trials with Bayesian Juries Another potential application is liability for the filing of false charges and frivolous lawsuits. Under the common law tort doctrine of malicious prosecution a person who is falsely accused of a crime may bring a lawsuit against the accuser. The harm here consists of a false investigation and the reputational and dignitary harms that follow from beingundercriminalinvestigation.Somewhatsimilarconcernsarisewiththe filing of frivolous lawsuits, and under Rule 11 of the Federal Rules of Civil Procedure,courtsmayimposefinancialliabilityonalitigant.Howwillingthe courtsshouldbetoenforcemaliciousprosecutionclaimsorissuepenaltiesis debated, because of concern that penalties may chill innocent victims of real crimesfromcomingforward. Theframeworkdevelopedhereisusefultotheanalysisofthesequestions, especially because judges and jurors sometimes consider one’s record (even whentheyoughtnotto)inassessingguiltorliability.Insuchcontexts,punishingfrivolouslawsuitsmoderatelymayhavethe(additional)benefitofmaking the trial process more accurate, and thereby amplify its deterrent effect by increasing the opportunity cost of engaging in wrongdoing. Although many additional dynamics can emerge in the trial context, especially in those resemblingthebilateralaccidentsframework,theimpactofpunishingfrivolous lawsuits can be re-visited from the perspective provided here by analogizing theplaintiff(orprosecutor)tothespeaker,thedefendanttothetarget,andthe jurytotheaudience. In fact, the framework provided in (Freidman & Wickelgren 2005) can be usedtoevaluatetheoptimalpenaltiesinfightingfrivolousclaims.Intheirarticle, Friedman and Wickelgren consider a context wherein jurors form beliefsregardingclaimsmadeagainstadefendantbasedontheevidencethatis presented at trial. They use their setting to establish an upper bound on deterrence,buttheyalsofindthatthisupperbounddependsonthequalityofthe evidencepresentedtojurors.Thefrequencyoffrivolousclaimsimpactstheaccuracywithwhichjurorsformopinions,and,thus,reducingitoughttoincrease theupperboundondeterrence.But,ofcourse,penalizingfrivolousclaimstoo severely can have the impact of deterring legitimate claims, which will have the opposite effect. Thus, as in our setting, the optimal penalty for frivolous 26 .V0N0 claimswouldhavetobemoderateandbalancethesetwoconsiderations. 5.5.4 Securities Regulation Public companies are required to disclose periodical reports about their performance to the public. These reports affect the propensityofinvestorstodealwiththereportingcompany,andthegoalofsecuritiesregulationistoregulatetheaccuracyofthesereportsgiventheinherent moralhazardcompanieshavetodistortinformation. Thiscontextissimilartotheframeworkdevelopedhere,wheretheaudience consistsofprospectiveinvestors, thecompanytakestheplaceofthespeaker, and the regulator assumes the position of the target (in deciding whether to bring a lawsuit).The question of optimal damages d, is akin to asking how stricttheagencyshouldbeinitsenforcementofthelaw,aswellasthelevelof finesthatitissues.Oneimmaterialdifferenceinthiscontextisthatthespeaker makesstatementsaboutitself,ratherthananotherparty.Thesecondandrelated differenceisthatthespeaker-companywouldnormallynotwanttodisparage itself;rather,itwouldseektopraiseitself.Thisdifference,however,haslittle analyticalsignificance,asitsimplyinvolvesreversingthelabelsinourinitial analysis. Applying the framework at hand to securities regulation could reveal, for example,whystrictandlaxenforcementisinferiortomoremoderateenforcement. It could also be useful in highlighting the importance of making information revealed by companies actionable and the conditions under which it is desirable to do so. Yet another potential insight concerns the importance of understanding judicial competency in any given area of disclosure and its relevancetothelevelofinformationregulation. 6. Conclusion Thelawregulatesinformationdisseminationinavarietyofcontexts.Work in this area has tended to focus on the effect of such regulation on speakers and their targets, and has not paid much attention to audience effects. In this articlewehighlighttheimportanceofaudienceeffectsbyshowingthatinthe presenceofBayesianaudiences,stricterregulationofinformationmayjeopardizeitsvalue.Whilelaxregulationresultsinnon-credible“cheaptalk,”strict regulationcanresultinequallyuninformative“overpricedtalk.” 7. Appendix Proof of Proposition 2 The proof begins with part (ii), which is used in provingpart(i). (ii)Weproceedbydemonstratingthattheonlyequilibriawheretheactions of the audience are not described by a∗(z) = z for all z are (1) those where theaudienceendsupalwaysinteractingwhenγ > x,and(2)thosewherethe (cid:98) audienceendsupneverinteractingwhenγ γ impliesthatx∗ < γ, becausex∗(1−µ(s∗))+ 0 1 0 x∗µ(s∗) = γ. Thus, x∗ (cid:62) x > γ implies that x > γ > x∗, which is a 1 0 (cid:98) (cid:98) 1 contradictionwithR1’simplicationthatx∗ (cid:62)x. 1 (cid:98) Suppose there is a PBE where a∗(z) = 1 − z for all z. Then, per R3, s∗(t,v) = 0 for all v and t, and, thus, the audience never interacts in such assessments. SupposethereisaPBEwherea∗(z) = 1forallz.Bydefinition,theaudienceneverinteractsinsuchassessments. (2)γ >x: (cid:98) SupposethereisaPBEwherea∗(z) = 0forallz.Bydefinition,theaudiencealwaysinteractsinsuchassessments. Suppose there is a PBE where a∗(z) = 1 − z for all z, then per R3, s∗(t,v) = 0 for all v and t, and, therefore, µ(s∗) = 0, which implies that Γ(t = G|0,s∗) = γ.ThisimpliesviaR4thatx∗ = γ,which,inturnimplies viaR1that a∗(0)=0,whichcontradictstheassumptionthata∗(0)=1. Suppose there is a PBE where a∗(z) = 1for all z. If µ(s∗) = i ∈ {0,1}, then Γ(t = G|i,s∗) = γ, which implies via R4 that x∗ = γ. This implies i viaR1thata∗(i)=0,whichisacontradictionwiththeinitialsupposition.If, on the other hand, µ(s∗) ∈ (0,1), observe that, per R4, x∗ (cid:54) γ implies that x∗ (cid:62) γ, because x∗(1−µ(s∗))+x∗µ(s∗) = γ. Thus, x∗ (cid:54) γ implies that 1 0 1 0 x∗ (cid:62)γ >x,whichisacontradictionwiththeimplicationofR1thatx∗ (cid:54)x. 1 (cid:98) 1 (cid:98) (1)and(2)togetherdemonstratethatallPBEwheretheactionsoftheaudience are not described by a∗(z) = z for all z involve the audience behaving accordingtoitspriors. (i)Considerdamagesd < l ,andsupposea∗(z) = z forallz.Itfollows viarequirement2thatp∗(t) = 2qG 0forallt.Thus,R3impliesthats∗(t,v) = 1 for all v and t, and, therefore, x∗ = γ due to R4 . Thus, in equilibrium, the audienceactsaccordingtoitspriors. Next,considerdamagesd > 2v−l.ItfollowsperR2thatp∗(t) = 1.Thus, 2qB per R3, s∗(t,v) = 0 for all v and t, because d > 2v−l. This implies via R4 that x∗ = γ. Thus, in equilibrium, the audience ac ts qB according to its priors. 0 (cid:104) (cid:105) The analysis of these two cases demonstrates that when d (cid:54)∈ l ,2v−l , in 2qG 2qB all PBE where a∗(z) = z for all z, the audience acts according to its priors. Inaddition,part(ii)ofthispropositiondemonstratesthattheaudienceactsaccordingtoitspriorsinallPBEwheretheaudience’sbehaviorisnotdescribed (cid:104) (cid:105) bya∗(z) = z.Thus,wheneverd (cid:54)∈ l ,2v−l ,theaudienceactsaccording 2qG 2qB toitspriorsinallPBE. (iii) Equilibria described (and whose existence are proven) in proposition 3-(i)andsection4.demonstratethatsuchdefamationlawsexistunderallcircumstances. ProofofProposition3(i)Considerdefamationlawswithd= 2v−l.Itcan easilybeverifiedthattheassesmentwherea∗(z)=zforallz;x∗ = qG ,x∗ =0; (cid:26) (cid:26) 0 1 1 if t=B 0 fort=B s∗(t,v) = forallv;andp∗(t) = sat0 if t=G 1 fort=G 28 .V0N0 isfiesR1-R4.Inthisequilibrium,thereisnolitigationbecauseifs∗(t,v)p∗(t)= 0foralltandv. (ii)Whent=G,thisequilibriumleadstoatotalpay-offofr+g,andwhen t = B,itleadstoatoalpay-offofv.Thesetwovaluesconstitutethehighest pay-offs that can be generated (see, e.g., figure 1) conditional on the target beingagoodtypeandabadtype,respectively,becauser+g >v >0>r−b. Thus,therecanbenoPBEthatleadstohigherpay-off. (cid:104) (cid:105) (iii) Consider imprecise courts. If d (cid:54)∈ l ,2v−l , the audience acts ac2qG 2qB cording to its priors in all equilibria as proven in proposition 2, and thus it either always interacts, which leads to bad interactions with a probability of 1 − γ; or it never interacts, which leads to no interactions with good types (cid:104) (cid:105) withaprobabilityofγ.Ifd ∈ l ,2v−l , thesameresultholdsinallPBE 2qG 2qB except, potentially, in PBE where a∗(z) = z for all z. Thus, consider next the interaction probabilities in equilibria where a∗(z) = z for all z when (cid:104) (cid:105) d∈ l ,2v−l . 2qG 2qB (cid:16) (cid:17) (a)Supposed∈ l ,2v−l : 2qG 2qG It follows per requirement 2 that p∗(G) = 1. Thus, per R3, s∗(G,v) = 1 if v >q d+ l G 2 for all v. This implies that, with probability γ(1− 0 if v 0, the audience does not interact with a good type in such G 2 PBE(ifthereexistany). (cid:16) (cid:105) (b)Supposed∈ l ,2v−l : 2qB 2qB It follows per R2 that p∗(B) = 1, and because d (cid:54) 2v−l it follows that 2qB 1 if v >q d+ l s∗(B,v) = B 2 for all v < v. This implies that with 0 if v 0, the audience does not interact with a good type in such G 2 PBE(ifthereexistany).Ifp∗(G) = 0,perR3,s∗(G,v) = 1forallv,which impliesthattheaudienceneverinteractswithagoodtypeinsuchPBE(ifthere existany). Thus,inallPBEobtainedthroughmoderatedamageswherea∗(z) = z for allz ,eithertheprobabilityofnointeractionwithagoodtypeispositive,the probabilityofinteractionswithabadtypeispositive,orboth. (iv) Let d = l . Consider an assessment where a∗(z) = z for all z, and 2qB REFERENCES 29 p∗(G)=1 and p∗(B)=0(satisfiesR2) (cid:26) 1 if v >q d+ l s∗(G,v)= G 2 and s∗(B,v)=1(satisfiesR3); where 0 if v x>x∗,whichguaranteesthattheassessment 0 (cid:98) 1 alsosatisfiesR1,andisthereforeaPBE. ItfollowsthattheexpectedwelfareassociatedwiththisPBEis q 1 q 1 l(q +q ) W(cid:99) =γ[F(l{ G + })(r+g)+(1−F(l{ G + }))E[v|v > G B ]]+(1−γ)E[v] 2q 2 2q 2 2q B B B (10) whereE[.]referstoexpectedvalues.Itfollowsthat lim W(cid:99) =γ(r+g)+(1−γ)E[v] (11) qG→π qB If,x > γ,welfareobtainedinequilibriawheretheaudienceactsaccording (cid:98) toitspriorsisE[v],andifx<γ,thewelfareobtainedinequilibriawherethe (cid:98) audienceactsaccordingtoitspriorsr−b<0.Because,r+g >v,itfollows that lim W(cid:99) >E[v]>r−b (12) qG→π qB Becausethefirstinequalityisstrict,thereexists qG <πsufficientlyclosetoπ qB suchthatW(cid:99)exceedsthewelfareobtainablewhentheaudienceactsaccording to its priors. Thus, when courts are only slightly imprecise there is a PBE associated with d = l which leads to greater welfare than PBE where the 2qB audienceactsaccordingtotheirpriors. References 1. Arbel, Yonathan A. and Mungan, Murat. 2019. The Uneasy Case for ExpandingDefamationLaw.AlabamaLawReview1-999 2. Acheson, D. 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