Cheap Talk with Two Audiences

When an informed party can engage in cheap talk with more than one audience, we show how the presence of one audience may either discipline or subvert the speaker's relationship with the other audience. We ask how welfare is affected by public or private disclosure, and predict how much communication will take place. Keyvt^ords. cheap talk, signaling, communication, incentives. Cheap Talk with Two Audiences Joseph Farrell and Robert Gibbons* When an informed party can engage in cheap talk with more than one audience, we show how the presence of one audience may either discipline or subvert the speaker's relationship with the other audience. We ask how welfare is affected by public or private disclosure, and predict how much communication will take place. Why are some claims made in public and others in private? Are public announcements always more credible than private ones? Should a politician meet with conservative and liberal constituents separately or together? How does it matter that a firm's claims about its profitability aff'ect both its bond rating and its labor negotiations? When there are two candidates for a promotion, could the boss improve the credibility of his claims about their prospects by talking to both candidates together rather than separately? Why are engagements and weddings public? Why are letters of recommendation private? These problems have in common a simple structure: an informed "sender" says something to two interested but uninformed "receivers," who then take actions based on their beliefs; these actions affect the sender as well as the receivers. In this paper we study how costless, nonverifiable claims [cheap talk) can affect these beliefs (and hence the actions), and how the incentives for truthful revelation to one receiver are affected by the presence of the other. We then ask how welfare is affected by whether claims axe made in public or in private. As some of the above examples suggest, public messages may be more credible than private messages addressed to either audience. One possibility is that the presence of one audience can discipline the sender's relationship with the other; we call this one-sided discipline. An analogous idea (although with costly signals rather than with cheap talk) 'Berkeley and Hoover, and MIT, respectively. We thank David Austen-Smith, Jeremy Stein, and workshop participants at Princeton and Hoover for helpful comments. This work was financially supported in part by the National Science Foundation through Grants IRI 87-12238 (Farrell) and SES 88-09200 (Gibbons) , by the Hoover Institution, and by the Industrial Relations Section at Princeton University. has been discussed in the finance literature by Sudipto Bhattacharya and Jay Ritter (1983) and Robert Gertner, Gibbons and David Scharfstein (1988). But, as we show below, onesided discipline is not the only interesting possibilitj', even in a very simple model. For instance, the presence of one audience may instead subvert the speaker's relationship with the other: credible communication may be impossible in public, though possible with one audience in private. Or, the infornied party may be unable credibly to communicate with either audience in private, but able to communicate in public: we call this mutual discipline. In Section I, we develop a simple model of cheap talk with two audiences. In Section II, we characterize the equilibria of our model, including those discussed above, and we give examples of some of the more interesting kinds of equilibria. In Section III, we consider the welfare implications of public or private disclosure. In Section IV, we analyze equilibriimi selection, and predict how much information will be revealed. Finally, in Section V, we discuss (A) some further examples, (B) two extensions of our analysis, and (C) a possible direction for further work. I . A Model We develop the simplest possible model of cheap talk with two audiences. A sender, S, observes the state of the world 5 € {^i, S2}; the (common-knowledge) prior probability of 5i is TT. There are two audiences or receivers, Q and R. (For pronominal clarity, we take 5 to be a man and Q and R to be women.) Each receiver can take an action: Q chooses Qi or ^2 5 2Ji<i R chooses r^ or fj . Each receiver's payoff depends on her own action and on the state of the world, s: for simplicity we suppose that it does not depend on the other's action. If one audience had an action that was always optimal for her irrespective of her beliefs about s, then the sender would not have to consider her reactions. Consequently, there would be in effect only one audience, and this problem has already been well studied by Vincent Crawford and Joel Sobel (1982). Without loss of interesting generality, therefore, we suppose that the receivers' payoffs are such that if the state were known to be 5^ then Q would choose g^ and R would choose r^. By normalizing, we can display these payoffs as in Table 1, and then our assumption is that Xi,X2,yi and j/j are all positive.