/*! J,V0N0 1 (ssrn-3452662) — corpus code wrapper This file intentionally embeds the paper text and study assets in code form. It helps code-centric ingestion pipelines and makes the corpus easy to load programmatically. */ pub const PAPER_ID: &str = "ssrn-3452662"; pub const TITLE: &str = r#"J,V0N0 1"#; pub const SSRN_URL: &str = r#"https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3452662"#; pub const YEAR: i32 = 2020; pub static AUTHORS: &[&str] = &[ r#"Yonathan Arbel"#, ]; pub static KEYWORDS: &[&str] = &[ r#"contracts"#, r#"AI"#, r#"law"#, ]; pub const SUMMARY_MD: &str = r#"Okay, here are the bullet points based on the provided text: * **Professor Yonathan Arbel of the University of Alabama School of Law argues that** regulations on information exchange often neglect how audiences adapt their beliefs and actions based on the strictness of laws governing statement veracity. His research addresses this "audience gap" by employing a Bayesian game to model interactions among speakers, targets, and audiences, specifically investigating how legal strictness influences their behavior and the overall information environment. 1. ## TL;DR ≤100 words Professor Yonathan Arbel of the University of Alabama School of Law argues that information regulation often overlooks how audiences adjust their beliefs and actions based on the strictness of laws governing statement veracity. His research aims to address this "audience gap" by using a Bayesian game to model interactions between speakers, targets, and audiences, particularly examining how legal strictness impacts their behavior and the resulting information landscape. 2. ## Section Summaries ≤120 words each * Professor Yonathan Arbel of the University of Alabama School of Law writes that the common approach to regulating information exchange has a significant blind spot: it often fails to account for the dynamic ways in which audiences adapt. Specifically, how audiences adjust their beliefs and subsequent actions is directly influenced by the perceived strictness of the laws that govern the truthfulness of statements. This oversight can lead to miscalibrated regulations. * Professor Yonathan Arbel of the University of Alabama School of Law writes that his research endeavors to fill this identified "audience gap" in the understanding of information regulation. To do so, he utilizes a Bayesian game framework. This model simulates the interactions between three key parties—speakers, the targets of statements, and the audiences receiving them—with a particular focus on how varying degrees of legal strictness regarding statement veracity shape the strategic behaviors of all involved."#; pub const SUMMARY_ZH_MD: &str = r#"好的，这是以上英文法律摘要的正式中文翻译： 以下是根据所提供文本整理的要点： * **阿拉巴马大学法学院的约纳坦·阿尔伯（Yonathan Arbel）教授认为，** 关于信息交流的规制往往忽视了受众会如何根据规制陈述真实性法律的严格程度来调整其认知和行为。他的研究通过运用贝叶斯博弈模型，对信息发布者、信息指向对象和信息受众之间的互动进行建模，旨在弥合这一“受众认知鸿沟”，并具体探究法律的严格程度如何影响各方行为及整体信息环境。 1. ## 内容概要（≤100字） 阿拉巴马大学法学院的约纳坦·阿尔伯教授指出，信息规制常忽视受众如何根据陈述真实性法律的严格程度调整其认知与行为。其研究旨在通过贝叶斯博弈模型分析信息发布者、指向对象及受众间的互动，以填补此“受众认知鸿沟”，并探究法律严格性如何影响各方行为及最终的信息格局。 2. ## 各节摘要（每节≤120字） * 阿拉巴马大学法学院的约纳坦·阿尔伯教授在其研究中指出，当前信息交流规制的普遍方法存在一个显著盲点：即未能充分考虑到受众动态调整其认知与行为的方式。具体而言，受众如何调整其认知及后续行为，直接受到其所感知的、规制陈述真实性的法律严格程度的影响。这种忽视可能导致规制措施的失当。 * 阿拉巴马大学法学院的约纳坦·阿尔伯教授在其研究中阐述，其研究致力于填补在信息规制认知领域中已识别出的这一“受众认知鸿沟”。为此，他运用了贝叶斯博弈框架。该模型模拟了信息发布者、信息指向对象及信息受众这三方主体间的互动，并特别关注不同严格程度的陈述真实性法律如何塑造所有参与方的策略行为。"#; pub const ONE_PAGER_MD: &str = r#"# J,V0N0 1 — one-page summary **Paper ID:** `ssrn-3452662` **Year:** 2020 **Author(s):** Yonathan Arbel **SSRN:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3452662 ## TL;DR Professor Yonathan Arbel of the University of Alabama School of Law argues that information regulation often overlooks how audiences adjust their beliefs and actions based on the strictness of laws governing statement veracity. His research aims to address this "audience gap" by using a Bayesian game to model interactions between speakers, targets, and audiences, particularly examining how legal strictness impacts their behavior and the resulting information landscape. ## Keywords contracts; AI; law ## Files - Full text: `papers/ssrn-3452662/paper.txt` - PDF: `papers/ssrn-3452662/paper.pdf` - Summary (EN): `papers/ssrn-3452662/summary.md` - Summary (ZH): `papers/ssrn-3452662/summary.zh.md` _Auto-generated study aid. For canonical content, rely on `paper.txt`/`paper.pdf`._ "#; pub const STUDY_PACK_MD: &str = r#"# Study pack: J,V0N0 1 (ssrn-3452662) - SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3452662 - Full text: `papers/ssrn-3452662/paper.txt` - Summary (EN): `papers/ssrn-3452662/summary.md` - Summary (ZH): `papers/ssrn-3452662/summary.zh.md` ## Elevator pitch Professor Yonathan Arbel of the University of Alabama School of Law argues that information regulation often overlooks how audiences adjust their beliefs and actions based on the strictness of laws governing statement veracity. His research aims to address this "audience gap" by using a Bayesian game to model interactions between speakers, targets, and audiences, particularly examining how legal strictness impacts their behavior and the resulting information landscape. ## Keywords / concepts contracts; AI; law ## Suggested questions (for RAG / study) - What is the paper’s main claim and what problem does it solve? - What method/data does it use (if any), and what are the main results? - What assumptions are doing the most work? - What are the limitations or failure modes the author flags? - How does this connect to the author’s other papers in this corpus? _Auto-generated study aid. For canonical content, rely on `paper.txt`/`paper.pdf`._ "#; pub const ARTICLE_TEXT: &str = r#"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,EzraFried- man,NunoGaroupa,AlexLee,BenMcMichael,AlanMiller,SepehrShahsha- hani, 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 pro- cessinformationdifferentlywhenitsveracityisstrictlyregulated.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,andweinvestigatetheimpactofthestrictnessofthelawontheemerg- ingPerfectBayesianEquilibria(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: Electronic copy available at: https://ssrn.com/abstract=3452662 2 .V0N0 claims about the target to an audience member. The audience member then decideswhethertointeract—trade,trust,socialize—withthetarget.Ifthetar- get loses an interaction, he may bring a lawsuit against the speaker. Within thisframework,itissociallyoptimalforaudiencestoonlyinteractwithhigh- quality 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)theaudiencemakesdecisionsinlightofthecontentofthesuppliedinfor- mation,(iii)thespeaker’sobjectiveconflictswiththatofanotherparty(thetar- get),and(iv)thelawpenalizesthesupplyoffalsenegativeinformationbythe speaker.Thesekeyfeaturesarepresentinmanycontexts,including: defama- tion law, whistle-blower rewards, complaint-driven law enforcement, and se- curities 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),wefocusondefamationlawasourrun- ningexamplewithprivateenforcementinourbaselinemodel(Sections3and 4).Wesubsequentlyextendtheanalysistocomparepublicandprivateenforce- ment,anddiscussspecificfieldsbesidesdefamationlaw(inSection5). Our analysis reveals five central findings. First, the harmful effect of dis- paraging statements is deeply related to the strictness of the law itself. A speaker’sstatementsmayinformtheaudience’sbeliefsandactions.Inchoos- ing whether to make disparaging statements, speakers will consider the ex- pectedcostofapotentiallawsuitagainstthem.Stricterlawsincreasethiscost. Thus, inequilibrium, thestrictnessofthelawaffectsspeakersand, anticipat- ingthis,alsotargetsandaudiences.Theseeffectssometimesresultincounter- intuitive implications, such that targets of speech who are ‘good’ types may preferlaxerlaws,eventhoughitwouldlimittheirrecoveryinasuccessfullaw- suit.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,speak- ersfrequentlymisstatethetruthandaudiencesrelymoreontheirpriorsrather 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 too great, and so speakers would refrain from sharing negative private infor- mation.Therefore,overlystrictlawsdeprivetheaudienceofmeaningfulinfor- Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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, impos- ingrelativelylargedamagesthatdeterfalsestatementscanleadtoseparating equilibriawhereonlytruthfulstatementsaremade.Usingthelawtoregulate informationcontinuestobeoptimalincaseswherecourtsdonothavetheac- curacynecessarytoimplementseparatingequilibria,but,candetermostfalse statementswithoutchillingtruthfulstatements.Whencourtsarelesscapableof accuratelyadjudicatingstatements,thesocialcostofusingthecourtsystem— operationalizedbylitigationcosts—iskeyindeterminingwhetherinformation shouldberegulated.Eveninthesecases,whenthegainsfromfacilitatingbene- ficialinteractionsanddeterringharmfulonesdwarfslitigationcosts,moderate damagesemergeastheoptimalchoice.2 Anotherimplicationpertainstothepotentialdynamicimpactofinformation regulating laws. Specifically, moderate laws that cause the audience to ratio- nally rely on speakers’ statements broadens the gap between the frequency withwhichtheaudienceinteractswithgoodtypesversusbadtypes.Thisnat- urally increases the returns from being a good versus a bad type, thereby in- centivizing individuals and firms to increase the quality of their products or services. Lastly, our comparison of public and private enforcement reveals the rela- tivemeritsofprivateenforcement.Apublicagencymaybeabletocommitin advancetoacertainlevelofenforcement.Whereasprivatepartiesarelessca- pableofcommitment,theyenjoyanaturalinformationaladvantageregarding the merit of the lawsuit, as they know their own type. Consequently, private enforcement leads to more accurate litigation decisions, and an intuitive ad- vantage of private enforcement emerges in our model: separating equilibria canonlybeachievedthroughprivateenforcement. Overall,ourframeworkandresultsaddtotheliteratureoninformationreg- ulation by spotlighting the importance of audience effects, offering a formal framework that accounts for audiences, and emphasizing the risks of overly- stringentandlaxregulatoryregimes. Thenextsectionofferssomebackgroundandreviewstherelatedliterature. Section3presentsthemodelanditsanalysiswithafocusoncaseswherethe courts are relatively accurate. Section 4 explains, in detail, the more compli- cated trade-offs that emerge when courts are not accurate enough to achieve separatingequilibria.Section5includesseveralpotentialextensionsoftheba- 1. Whenweconsiderhonestandothertypesofspeakers,wealsoshowthatstrictlawscanbe worsethanlaxones,forsimilarinformationalreasons. 2. Incidentally,thisconclusioncanofferarationaletothelongstandingdistinctionindefama- tionlawbetweenfactsandopinions,whicharegenerallyunregulated. Electronic copy available at: https://ssrn.com/abstract=3452662 4 .V0N0 sicmodel,suchasthepublicenforcementcase,thegeneralizationofthemodel tocaseswherespeakersmaybemotivatedtospeaktruthfullyortoexcessively praisethetarget, anddiscussionsofcontextsotherthandefamationlaw.Sec- tion6providesconcludingremarks. 2. Backgroundandrelatedliterature Variouslawsregulateinformationbysanctioningfalsedisclosureorreward- ing truthful sharing of information. Defamation is a classic example of the formerandwhistle-blowersofthelatter.Theliteratureonthesetopicsisdis- parate, but contain the same question: How to design sanctions and rewards that would incentivize the optimal sharing of information. A common recur- ring omission is the possibility that the audience may update its beliefs, in a Bayesianmanner,basedonthesizeofthesanctionsorrewards.Becauseofthe fragmentednatureoftheliterature,wewillconsiderfourexamples. Defamationlawisperhapsthequintessentialexampleoftheproblemofin- formationregulationandthusservesasourrunningexample.Underdefama- tionlaw, atargetofa(1)publicstatementthatis(2)falseand(3)harmfulto one’sreputation,cansueforallresultingdamages.Judgmentsinthisareacan resultinhighpayments, withsomecasesreportingjuryjudgmentsoftensof millions of dollars (Lesher v. Does, 2013). While courts and legislators un- derstandthebehavioraleffectsofdefamationlaw,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&Re- falo, 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-blowerstoanenforce- mentagency(Givati, 2016,Buccirossietal.2017,Deoorter&DeMot, 2005). Onefindingisthatwhentheriskoffalsereportingishigh,itmightbeneces- sarytoavoidrewardingwhistleblowersaltogether,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 capturedinthestandardlawandeconomicsliterature(forareview,seePolin- Electronic copy available at: https://ssrn.com/abstract=3452662 -- 5 skyandShavell2017),whichtypicallyreliesonmodelswheretheprobability ofdetectionisonlyafunctionofenforcementexpenditures.Inreality,thepo- lice 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 self- reports its performance, under an enforcement threat by the Securities and ExchangeCommission(SEC).Theliteraturerecognizesthattheagency’sen- forcementcanbeanimportantcredibilitymechanism(Stulz2009),butitpays littleattentiontohowstrictenforcementinteractswithinvestorsandthetrust theyplaceincompanydisclosure. Methodologically, our article borrows tools from the rich literature on sig- naling(Spence1973)andcheaptalk(Crawford&Sobel, 1982).Ouranalysis canalsobeinterpretedaspartofanemergingliteraturethatlooksathowlaws canbeusedtocreateinformalsanctionsthroughthebehaviorofthirdparties (e.g.,Deffains&Fluet, 2019,Mungan2016,Be´nabou&Tirole, 2011,2006, Rasmusen1996.) 3. Model Tostudythebehavioraleffectsofinformationregulationwefocusontheex- ampleofdefamationlaw,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 ei- therdisparageT ormakeanon-disparagingcomment.Asweareinterestedin defamation,weassumethatS mightbenefitfromblockinganinteractionbe- tweenAandT,andsoSmaychoosetodefameT–i.e.,liethatT isabadtype3. Ofcourse,manyspeakersmaybemotivatedbyadesiretospeaktruthfullyor tofacilitateinteractionsbetweenT andA,andweconsiderthispossibilityin section5.2. WemodeltheinteractionsasaBayesiangame,anduseittoidentifyPerfect Bayesian Equilibria. Figure 1, below, depicts the interactions between these threepartiesandishelpfulinfollowingthedetaileddescriptionsoftheinter- actionsthatweprovide,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.How- ever,thecourtmaymakeerrorsinascertainingwhetheranegativestatementistruthful,andthis possibilityisincorporatedinourmodel,asweexplainbelow. 4. ThefiguredoesnotdepictNature’sdrawofS’stype,duetoreasonsweexplain,below. Electronic copy available at: https://ssrn.com/abstract=3452662 6 .V0N0 Figure1Extendedgametreeofthemodel. Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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 in- teractwithAandobtainsabenefitofrfromtheinteraction.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 non- actionable(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 Electronic copy available at: https://ssrn.com/abstract=3452662 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 re- quirementsthatpertaintoT 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 im- plied conditional probability of T being a particular type based on the equi- libriumstrategyofS.Thisrequirementisapplicableonlytostrategieswhich haveapositiveprobabilityofbeingplayedbyS. Ouranalysisrevealsthattherearetwotypesofassessmentswhichsatisfyre- quirements1-4,i.e.twotypesofequilibrium.One,inwhichthespeaker’sstate- mentshavenobearingontheaudience’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 ambigu- ities 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 not- ing 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 Electronic copy available at: https://ssrn.com/abstract=3452662 -- 11 behavior,werelyonourbehavior-baseddefinitionofeffectivecommunication equilibria. 3.4 ImpactofDefamationLawsonEquilibriumBehavior ByusingRequirements1-4weidentifyandinterpretthePBEobtainedwith different damages, through the help of four propositions, below. Our obser- vations can be briefly summarized as follows. Proposition 1 shows that, re- gardlessofthelevelofdamages, therearealwaysineffectivecommunication equilibria where A acts according to its priors, i.e., where A essentially ig- noresthecontentofSsstatement.Intheseequilibria,partiescannoteffectively communicateprivateinformation.Infact.whendefamationlawsareextreme, i.e. either too lax or too strict, ineffective communication equilibria are the onlyPBEofthegame, aswenoteviaProposition2.Onlymoderatedefama- tionlawscanengendereffectivecommunicationequilibria.Then,wequestion whethereffectivecommunicationequilibriaaresociallypreferabletoineffec- tiveones.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 en- hancewelfarethroughmoderatedamagesthroughsemi-separatingequilibria. Finally, Proposition 4 reveals that when the value of A’s returns from inter- actionsdwarfsotherconsiderations,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,bydefini- tion,interactionnevertakesplace.ButthenS canprofitablydeviatefromher Electronic copy available at: https://ssrn.com/abstract=3452662 12 .V0N0 strategy s∗ by choosing not to defame whenever t = G and v < q d+ l. G 2 Thus,litigationcannotbetakingplaceinanineffectivecommunicationequi- librium. Proposition 1 reveals that it is always possible in equilibrium for the audi- encetoactaccordingtoitspriors.GiventhisresponsebyA,S hasnothingto gainbydisparagingthepotentialplaintiff,becauseherstatementshavenoef- fectonA’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 identifyingfourcriticaldamagelevelswhichplayakeyroleintheinterpreta- tionofresults.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’sincen- tives(i.e. l < 2v−l fori∈B,G),givenourassumptionthatlitigationcosts 2qi 2qi arenotprohibitivelyhigh,i.e.l 2v−l,itfollowsthatalleffectivedisparaging 2qB Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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 observationshighlightthatextremedamagescanonlyleadtoineffectivecom- munication PBE. A question that remains is whether moderate damages can lead to effective communication equilibria. Proposition 2 answers this ques- tionaffirmativelyandformalizesrelatedobservations. Proposition2. (i)Extremedefamationlawsonlygenerateineffectivecom- municationequilibria.(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 effec- tivecommunicationequilibria. Proof. SeeAppendix. Proposition2holdsthatextremedefamationlawsonlyallowforineffective communicationequilibria,and,asnotedinproposition1,theseequilibriaalso exist under moderate defamation laws. However, moderate defamation laws alsogenerateeffectivecommunicationequilibria.Thisimpliesthatswitching fromanextremedefamationlawregimetoamoderateregimecanexpandthe typesofequilibriathatmaybeobtained.Thus, itbecomesimportanttocom- parethepropertiesofthetwotypesofequilibriatoascertaintheirwelfareim- pacts,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:Whenthecourtissufficientlyac- curate(i.e. qG (cid:62) π)therearemoderatedefamationlawsassociatedwithPBE qB where: S disparagesT if,andonlyif,heisabadtype;theaudienceactscon- sistentlywiththisinformation(i.e.a∗(z) = z); andthereisnolitigation.(ii) Separating equilibria lead to greater expected welfare than all other equilib- ria.(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. Electronic copy available at: https://ssrn.com/abstract=3452662 14 .V0N0 slightly inaccurate, i.e. π − qG > 0 is sufficiently small, there exist moder- qB 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 am- qB 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 maxi- mizewelfare,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 con- tinuity 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 distin- guishinggoodandbadtypes,moderatedefamationlawscanbeusedwithrel- ativeeasetoenhancewelfareandtoincreasetheinformationalvalueofstate- ments made by speakers. In these cases, (semi-)separating equilibria lead to obviousandunambiguousimprovementscomparedtoequilibriawheretheau- dienceislefttouseitspriorstomakedecisions.Inpractice,however,thereare manycaseswherethereisexpressedconcernamongjudgesandlawyersthat discoveringthetruthisdifficultandthatlitigationisfraughtwithinaccuracies. Theanalysisinthenextsectionthusfocusesonthesesituations. Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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)cangener- ateatrade-offbetweencostsassociatedwiththesetwotypesoferrorsandmay alsoimpactexpectedlitigationcosts.Inthissection, wedescribethesetrade- offs. We focus exclusively on moderate defamation laws and the impact of changingdoneffectivecommunicationequilibriabecause,asnotedinPropo- sition 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 dam- agescontinuestobesociallypreferabletohavingextremedefamationlaws. Toexplainthedynamicsthatemerge,wefirststartbycalculatingtheequi- libriumbeliefs,i.e.x∗ andx∗ thatwouldemergeinaPBEwherea∗(z) = z, 0 1 assuming that such an equilibrium exists. We plot these beliefs in Figure 4, below,throughaspecificbutrepresentativeexample.Thehorizontalaxisrep- resentsdamages, onwhichwemarkthefourcriticaldamageslevelslistedin Figure2.Thistime,however,thecourt’saccuracyislowerthanπ,sotherank- ingoftheintermediatecriticaldamages(i.e. l and 2v−l)istheoppositeof thatdepictedinFigure3.Inadditiontoplottin 2 g qB beliefs, 2 i q . G e.,x∗andx∗,inFig- 0 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 0 a target who is disparaged may or may not be a good type, but is no more likelytobeagoodtypethanarandomdrawfromthepopulation,i.e.x∗ < γ. 1 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 1 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 Electronic copy available at: https://ssrn.com/abstract=3452662 16 .V0N0 Figure4. IllustrationofBeliefsandtheLikelihoodofaDisparagingStatement. Damages=d,x∗ 0 ,x∗ 1 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,evenifherbenefitfromblockinginteractionsismaxi- mal,i.e.v.Shewillonlydisparagebadtypesifherbenefitfromblockinganin- teractionissufficientlyhigh.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.Inthelower- moderate range (i.e. ( l , l )) damages are insufficient to completely pre- 2qG 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 Electronic copy available at: https://ssrn.com/abstract=3452662 -- 17 in this range generates more meaningful trade-offs by increasing the likeli- hoodofbeneficialinteractionsaswellasharmfulinteractions,whilereducing the likelihood of litigation. Thus, it is desirable to increase damages in this rangeonlyifthesavingsfromlowerlitigationcostsandtheincreasedvalueof beneficialinteractionsexceedthecostinvolvedwithharmfulinteractions.Ab- sent 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,butarenotsuf- ficiently 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,socialwelfareisim- provedbyreducingdamagesinthisrange. 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 speakercanbehelpfulinpromotingbeneficialinteractionsordissuadingharm- fulones.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. Thereexistmoderatedamagesleadingtoeffectivecommu- nicationequilibria,whichgenerategreaterwelfarethanineffectivecommuni- cationequilibria,aslongasgandbarelargerelativetoothercostsandbenefits. Electronic copy available at: https://ssrn.com/abstract=3452662 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-offsthattheau- diencewouldhavereceivedbyactingaccordingtoitspriors,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-offoftheaudiencestemmingfromamovefromaPBEwhereitactsac- cordingtoitspriorstoonewhereitactsaccordingtotheinformationitreceives 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 com- parison to other considerations, like litigation costs and the benefits that the speakergetsfromblockinginteractions,moderatedefamationlawscanbeused toenhancewelfare.Thisisbecause,undertheseconditions,thedominantcon- siderationbecomesthemaximizationoftheaudience’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,weabstractedfrommanyissuesthatbearontheregulationofin- formationinmoregeneralsettings,particularly,thepossibilityofacommitted publicenforcer,qualitybeingendogenouslychosenbythetarget,andtheexis- tenceofhonestandothertypesofspeakers.Hereweturnourattentiontothese issues. 5.1 EndogenousTypesandDynamicEfficiencies Inouranalysisthusfar,weassumedthatthetarget’stypetwasexogenously determinedbynaturetobeeitherGorBwithprobabilitiesγand1−γ,respec- tively.Onemightquestiontherealityofthisassumption,aspeoplecanmake investmentsthatwouldmakethembetterorworsetradingpartners, e.g., cre- atehigherqualityproducts,maintainsafetystandards,orkeephigherhygiene standards. One option of incorporating quality investments into our analysis is to re- place 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.More- c→0 c→∞ over,tokeepthedescriptionofthisextensionbrief,wefocusonthecasewhere Electronic copy available at: https://ssrn.com/abstract=3452662 -- 19 γ >x. (cid:98) Thequalityinvestmentdecisionisnowpartofalargergame.Givenanysub- gameequilibrium,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.Theintuitionunderlyingourresultsarestraightfor- ward.Extremelawsleadtoineffectivecommunicationequilibria.Incontrast, moderate laws create an environment with more reliable information regard- ing types, thus generating a greater gap between the payoffs obtainable by goodtypesversusbadtypes.This,inturn,increasesthereturnsfrombeinga goodtype,andleadstomoreinvestments.Inrealisticsettings,providingsuch additionalincentivesissociallydesirablewhenthepotentialinvestorisunder- incentivized 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 sev- ering the relationship between the audience and the target. This abstraction followstheideaofspeaker’s’bias’inthecheaptalkliterature.Inreality,how- ever,somespeakersmaynothavesuchmotivations.Quiteimportantly,many Electronic copy available at: https://ssrn.com/abstract=3452662 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 distin- guishbetweenthefirsttype, “truthspeakers,”thelattertype, “eulogists,”and theonesweformerlydiscussedinSection3as“disparagers.”Webriefly,and informally, explain now what occurs when these kinds of speakers are incor- poratedintoouranalysis. Inourdiscussion,weconceiveofthesetypesasfollows.Disparagers,aswe noted,receiveapositivevaluefromblockinganinteraction;truth-speakersare indifferent with respect to whether the parties will interact but receive some valuefromspeakingtheirmind; and,eulogistsreceiveavaluefromtherebe- inganinteraction.Therefore,solongascostsofsodoingarenothigh,dispar- agers 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). Theincorporationofthesetypesofspeakershasnoimpactontheobserva- tionthatextremelystrongdefamationlawsleavetheaudiencetoactupontheir priors. This follows, because once a critical threshold of damages is passed, disparagers as well as truth speakers are deterred from making negative re- marks.Thus,extremelystrongdefamationlawscausedisparagers,truthspeak- ers, 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,disparagingstatementsarestillsomewhatinforma- tive:Giventheexistenceofsometruth-speakers,thereissomeprobabilitythat any negative statement is true. Consequently, an audience that hears a nega- tive statement evaluates its credibility based on the ratio of truth-speakers to disparagers.Thus, (inanassessmentwherea∗(z) = z)wecanformulatethe audience’sbeliefthatthetargetisagoodtype,conditionalonanegativestate- mentasx∗ = 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 eulo- gists.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 dis- paraging and non-disparaging statements are somewhat informative of types. Inotherwords,non-disparagingstatementsaremoreindicativeofgoodtypes than no information at all (x∗ > γ), and disparaging statements are more 0 indicativeofbadtypesthannoinformationatall,i.e.x∗ <γ.Thus,iftheau- 1 dience’snecessarylevelofconfidenceforinteraction,(x),iscloseenoughtoγ (cid:98) Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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 ex- tremedamages.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 in- 1 0 crease,i.e.itcausesinformationsuppliedbyspeakerstobemoreinformative. This observation reveals another of our results that carries over in a modi- fied 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 im- mediatelyfollowsthatx∗ = 0, suchthatadisparagingstatementisperfectly 1 informative. Thepresenceofeulogists,however,meansthatx∗ <1.Thus,fullyseparat- 0 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.Strictlawsleadtocompletelyuninformativespeechinequilib- riumwhereaslaxlawsstillallowspeechtobesomewhatinformative,permit- tingeffectivecommunicationequilibria. 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, andthiscalculusexposesthemtostrate- gicbehaviorbywould-bedefamers.Incontrast,someparties,typicallypublic agencies, maybeabletocommitex-antetosue, evenifitdoesnotpaytodo soex-post.Comparingprivateandpublicenforcementcanbeusefulinunder- standing other contexts where information is regulated, and may also illumi- natethereasonswhyprivateenforcementisusedindefamation. Electronic copy available at: https://ssrn.com/abstract=3452662 22 .V0N0 Tohelpinthiscomparison,weconsiderasimplemodificationofouranal- ysis 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,whichisbyassumptionun- observable,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 behav- ior, as a lawsuit is possible even when expected damages are low. We next explainthebehaviorofthespeakerineffectivecommunicationequilibria,un- der 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,privateenforce- mentdominatespubicenforcementintermsofitswelfareconsequences.The differenceinthewelfareobtainableunderthetworegimesisenhancedfurther bythefactthatunderpublicenforcement,theenforcementagency’scommit- ment results in some litigation whenever defamation laws are effective (i.e. 2v¯−pl >d). 2pqB Thelastpointhighlightsamoregeneralandimportantadvantageofprivate enforcement over public enforcement. Specifically,private enforcement dele- gates 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 state- mentstobemoreinformativeofthetarget’stype. Insum,thiscomparisonilluminatetherelativevalueofpublicversuspublic enforcement.However,asourfocushereisoncommitment,weabstractfrom otherrelevantconsiderations, suchastherelativecostsoflearningaboutdis- paragingremarksorproducingevidence.Inasmuchaspublicagenciesemploy discretion, they are also susceptible to capture and other public choice prob- lems.Theseconsiderationsshouldalsobetakenintoaccountincomparingthe relative social desirability of pubic versus private enforcement in regulating speech. 5.4 FeaturesofDefamationLaw Ouranalysistookthedomainofpotentiallydefamatorystatements—disparaging remarks—asgiven.However,theframeworkdevelopedherecouldalsobeused toshedlightonsuchdeterminations,inparticular,thefactv.opinionandper- se v. pro-quod distinctions. Defamation law renders expressions of opinion non-actionable.Theanalysissuggestsarationale: itishardertodeterminethe truth-valueofopinions,leadingtogreaterjudicialinaccuracyandmakingreg- ulationlessvaluable.Itisalsopossiblethatthelawimplicitlyrecognizesthat Electronic copy available at: https://ssrn.com/abstract=3452662 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, andwefocusedondefama- tionlawduetoitscurrentimportance.Herewediscussthreeotherimportant settingswherethesekeyfeaturesarepresent: lawenforcement,jurytrials,and whistle-blowers.Thenwediscussanadditionalcontext,securitiesregulation, wherethespeakerrevealsinformationaboutitself.Despitethisconceptualdif- ference,thecurrentframeworkprovesilluminatinginconsideringtheoptimal regulatoryframework. 5.5.1 BayesianPublicEnforcers Newsaboutcrimeswhichwerecommitted after the police chose to ignore reports of abuse and other red flags are, un- fortunately, 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,enforcersactastheaudi- ence. 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,inturnhastheeffectofincreasingdeter- renceby 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 Electronic copy available at: https://ssrn.com/abstract=3452662 -- 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 incen- tivize people with abnormally high costs. In analyzing this problem, one can think of whistleblowers as speakers and law enforcement agencies as the au- dience.Theagencydilemmaishowtosetrewardsandpenaltiesinawaythat would allow for the effective transmission of private information without in- volvingtoohighverificationandlitigationcosts. 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,punish- ingfrivolouslawsuitsmoderatelymayhavethe(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 re- semblingthebilateralaccidentsframework,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.Intheirar- ticle, Friedman and Wickelgren consider a context wherein jurors form be- liefsregardingclaimsmadeagainstadefendantbasedontheevidencethatis presented at trial. They use their setting to establish an upper bound on de- terrence,buttheyalsofindthatthisupperbounddependsonthequalityofthe evidencepresentedtojurors.Thefrequencyoffrivolousclaimsimpactstheac- curacywithwhichjurorsformopinions,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 Electronic copy available at: https://ssrn.com/abstract=3452662 26 .V0N0 claimswouldhavetobemoderateandbalancethesetwoconsiderations. 5.5.4 Securities Regulation Public companies are required to disclose peri- odical reports about their performance to the public. These reports affect the propensityofinvestorstodealwiththereportingcompany,andthegoalofse- curitiesregulationistoregulatetheaccuracyofthesereportsgiventheinherent 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,whystrictandlaxenforcementisinferiortomoremoderateenforce- ment. It could also be useful in highlighting the importance of making infor- mation 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,stricterregulationofinformationmayjeopar- dizeitsvalue.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,theaudi- enceneverinteractsinsuchassessments. (2)γ >x: (cid:98) SupposethereisaPBEwherea∗(z) = 0forallz.Bydefinition,theaudi- encealwaysinteractsinsuchassessments. 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 0 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 0 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)togetherdemonstratethatallPBEwheretheactionsoftheaudi- ence 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 1 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 2 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)ofthispropositiondemonstratesthattheaudienceactsac- cordingtoitspriorsinallPBEwheretheaudience’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.demonstratethatsuchdefamationlawsexistunderallcir- cumstances. ProofofProposition3(i)Considerdefamationlawswithd= 2v−l.Itcan easilybeverifiedthattheassesmentwherea∗(z)=zforallz;x∗ = 2 1 qG ,x∗ =0; (cid:26) (cid:26) 0 1 1 if t=B 0 fort=B s∗(t,v) = forallv;andp∗(t) = sat- 0 if t=G 1 fort=G Electronic copy available at: https://ssrn.com/abstract=3452662 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 ac- 2qG 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 Electronic copy available at: https://ssrn.com/abstract=3452662 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 Ex- pandingDefamationLaw.AlabamaLawReview1-999 2. Acheson, D. J.; Wohlschlegel, A. (2018). The economics of weaponized defamationlawsuits.SouthwesternLawReview,47(2),335-384. 3.Be´nabou,Roland,andJeanTirole.2006.IncentivesandProsocialBehavior. AmericanEconomicReview96.5,1652-1678. 4.Be´nabou,Roland,andJeanTirole.2011.LawsandNorms.NationalBureau ofEconomicResearchNo.w17579. 5.Bar-Gill,OrenandAssafHamdani.2003.OptimalLiabilityforLibel.Con- tributionsinEconomicAnalysis&Policy.2(1) Electronic copy available at: https://ssrn.com/abstract=3452662 30 .V0N0 6. Buccirossi, Paolo, Giovanni Immordino, and Giancarlo Spagnolo. 2017. Whistleblower Rewards, False Reports, and Corporate Fraud. CEPR Dis- cussionPaperNo.DP12260 7. Crawford, Vincent and Sobel, Joel 1982. Strategic Information Transmis- sion.Econometrica50,143151. 8. Dalvi, Manoj and James F. Refalo. 2007. An Economic Analysis of Libel Law.EasternEconomicJournal.74-94 9. Depoorter, Ben and Jef De Mot. 2005. Whistle Blowing. Supreme Court EconomicReview,2-28. 10.Deffains,BrunoandClaudeFluet.2019.SocialNormsandLegalDesign. JournalofLaw,Econ.,andOrganizations1-31 11.Friedman,Ezra,andAbrahamL.Wickelgren.2005BayesianJuriesandthe Limits to Deterrence. Journal of Law, Economics, and Organization 22.1: 70-86 12.Hemel,DanielandArielPorat.2019.FreeSpeechandCheapTalk.Journal ofLegalAnalysis46-103 13. Garoupa, Nuno. 1999. Dishonesty and Libel Law The Economics of the ”Chilling”Effect,JITE284-300 14.Garoupa,Nuno.1999,TheEconomicsofPoliticalDishonestyandDefama- tion,InternationalReviewofLawandEconomics167-180 15.Givati,Yehonatan.2016,ATheoryofWhistleblowerRewards,Journalof LegalStudies43-72 16.Heymann,LauraA.2012.TheLawofReputation,andtheInterestofthe Audience,B.C.L.Rev.1341-1999 17.McNamara,Lawrence.2007.ReputationandDefamation 18.Mungan,MuratC.2016.AGeneralizedModelforReputationalSanctions and the (ir)Relevance of the Interactions between Legal and Reputational sanctions.InternationalReviewofLawandEconomics46.86-92. 19. Polinsky, A. Mitchell, and Steven Shavell. 2007. The Theory of Public EnforcementofLaw.HandbookofLawandEconomics1: 403-454. 20.Rasmusen,Eric.1996.Stigmaandself-fulfillingexpectationsofcriminal- ity.TheJournalofLawandEconomics39(2)(1996),519-543. 21.Spence, Michael.1973.JobMarketSignaling.QuarterlyJournalofEco- nomics87(3),355-374. 22.Steenson,Mike.PresumedDamagesinDefamationLaw.WilliamMitchell LawReview40(4)(2014),1492-1542 Electronic copy available at: https://ssrn.com/abstract=3452662 REFERENCES 31 23.Renee´.Stulz,SecuritiesLaws,Disclosure,andNationalCapitalMarketsin the age of Financial Globalization, Journal of Accounting Research, 2009, v47(2),349-390. Electronic copy available at: https://ssrn.com/abstract=3452662"#; #[derive(Clone, Debug)] pub struct Paper<'a> { pub paper_id: &'a str, pub title: &'a str, pub ssrn_url: &'a str, pub year: i32, pub authors: &'a [&'a str], pub keywords: &'a [&'a str], pub summary_md: &'a str, pub summary_zh_md: &'a str, pub one_pager_md: &'a str, pub study_pack_md: &'a str, pub article_text: &'a str, } pub fn as_paper() -> Paper<'static> { Paper { paper_id: PAPER_ID, title: TITLE, ssrn_url: SSRN_URL, year: YEAR, authors: AUTHORS, keywords: KEYWORDS, summary_md: SUMMARY_MD, summary_zh_md: SUMMARY_ZH_MD, one_pager_md: ONE_PAGER_MD, study_pack_md: STUDY_PACK_MD, article_text: ARTICLE_TEXT, } } fn main() { print!("{}", ARTICLE_TEXT); }