Strategic Communication with Lying Costs

1 Strategic Communication with Lying COSTSNAVIN KARTIKC olumbia University and University of California, San DiegoE-mail study a model of Strategic Communication between an informed Sender and anuninformed Receiver. The Sender bears a cost of Lying , or more broadly, of misrepresentinghis private information. The main results show that inflated language naturally arises in thisenvironment, where the Sender (almost) always claims to be a higher type than he would undercomplete information. Regardless of the intensity of Lying cost , there is incomplete separation, with some pooling on the highest messages. The degree of language inflation and how muchinformation is revealed depends upon the intensity of Lying cost .

2 The analysis delivers a frame-work to span a class of cheap talk and verifiable disclosure games, unifying the polar predictionsthey make under large conflicts of interest. I apply the model to highlight how the degree ofmanipulability of information can affect the tradeoff between delegation and : December 12, 2008 (First version: November 2003).Key words and Talk, Signaling, Misreporting, Exaggeration, Disclosure, Persuasion, paper subsumes portions of an earlier manuscript circulated as Information Transmission with Almost-CheapTalk. The other parts of that manuscript are now superseded by Selecting Cheap-Talk Equilibria, with YingChen and Joel research grew out of my dissertation, and I am indebted to my advisors, Doug Bernheim and SteveTadelis, for their generous support and advice.

3 I am also grateful to Vince Crawford and, especially, Joel Sobelfor encouragement and numerous conversations. I thank David Ahn, Nageeb Ali, Yeon-Koo Che, Wouter Dessein,Peter Hammond, Crist obal Huneeus, Maxim Ivanov, Jon Levin, Mikko Packalen, Ilya Segal, Jeroen Swinkels, BobWilson, a number of seminar and conference audiences, the Editor (Andrea Prat) and two anonymous referees forhelpful comments. Chulyoung Kim provided able research assistance. I gratefully acknowledge financial supportfrom a John M. Olin Summer Research Fellowship, a Humane Studies Fellowship, the National Science Foundation,and the Institute for Advanced Study at Princeton.

4 I also thank the Institute for its Communication with Lying Strategic transmission of private information plays an important role in many areasof economics and political science. Most theoretical studies of direct Communication can beclassified into the following two categories. One approach, initiated byGrossman(1981) andMilgrom(1981), assumes that information is verifiable and agents can withhold information butnot lie. These are referred to as games of persuasion or verifiable disclosure. The secondapproach, pioneered byCrawford and Sobel(1982) andGreen and Stokey(2007, circulated in1981), assumes that information is unverifiable and an agent can lie arbitrarily without directcosts, typically referred to as games of cheap talk.

5 These are two extremes in a continuum of possibilities. Rather than Lying synonymousin this paper with misrepresentation or misreporting being completely costless or prohibitivelycostly, reality usually lies in between: individuals can and do misrepresent private information,but bear some cost in doing so. These Costs arise for various reasons. First, there may beprobabilistic ex-post state verification that results in penalties if misreporting is detected, suchas random audits on taxpayers ( and Sandmo,1972). Second, there may be costsof manipulating information or falsifying a message, such as when a manager has to spend time cooking the numbers or otherwise expend costly resources in order to report higher profits ( and Weinberg,1989;Maggi and Rodriguez-Clare,1995).

6 Third, recent experimental worksuggests that people have an intrinsic aversion to Lying , even though messages areprima faciecheap talk (Gneezy,2005;Hurkens and Kartik,2008;S anchez-Pag es and Vorsatz,2006).This paper studies the classic Strategic Communication setting ofCrawford and Sobel(1982) (hereafter CS), with the innovation that some messages entail exogenous or direct lyingcosts for the Sender. I use the term Lying Costs to broadly capture a class of misrepresentationcosts, such as those discussed above. To fix ideas, here is a simplified version of the modelpresented in Section2: a Sender is privately informed about his type,t [0,1], and must senda message to the Receiver, who then takes a decision which affects both players payoffs.

7 Thereis a conflict of interest because the Sender wants the Receiver to believe that his type is higherthan it actually is. I suppose that for each Sender type,t, there is a set of messages,Mt, withthe interpretation that any messagem Mthas the literal or exogenous meaning my type ist. In this framework, the Sender is said to be Lying when he sends a messagem Mt for somet 6=t, and the magnitude of a lie can be measured by the distance between his true type and thetype he claims to be. When typetsends a messagem Mt , he bears a costkC(t , t), wherekis a scalar that parameterizes the intensity of Lying cost .

8 Ifk= 0, messages are cheap talk, andthe setting reduces to that of CS. This paper is concerned withk >0. Assume that for anyt,it is cheapest to tell the truth, and moreover, the marginal cost of a bigger lie is increasing in themagnitude of the Communication with Lying COSTSL ying Costs transform the CS cheap-talk model into one of costly signaling, althoughthe induced structure is different from traditional monotonic signaling games (Cho and Sobel,1990). The main results I provide concern the amount of information revealed by the Senderin equilibrium, and the language the equilibrium mapping from types to messages throughwhich information is transmitted.

9 For most of the paper, I focus on a tractable and appealingclass of Perfect Bayesian equilibria, described in structure of these equilibriais simple: low Sender typesseparate, revealing themselves through their equilibrium message,whereas high types segment into one or more connectedpools. The equilibria featurelanguageinflationin the sense that (almost) every typetsends a messagem Mt for somet > t. Thatis, the Sender (almost) always claims to be a higher type than he truly is, even though he suffersa cost of Lying . Of course, the Receiver is not systematically deceived, because she recognizesthat the Sender is inflating his messages and adjusts her decision accordingly.

10 While this stateof affairs may appear paradoxical at first glance, the key point is that if the Sender were to tellthe truth ( send a messagem Mtwhen his type ist), the Receiver would infer that histype is in factlowerthan it actually is, since she expects messages to be inflated. There is thusan inescapable inefficiency for the Sender in equilibrium, reminiscent of unproductive educationsignaling inSpence(1973) or dissipative advertising inMilgrom and Roberts(1986a).Language inflation is difficult to explain in a framework of pure cheap talk, due to theindeterminacy of language in any cheap-talk game. Yet, the phenomenon occurs in numeroussettings of Communication with conflicts of interest.