Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’

Abstract

We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication. When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to “whitewash” the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a “neutral historian” who verifies the truthfulness of others’ reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs. We also analyze a centralized communication protocol in which history leaves a “footprint” that can only hidden by the current cohort by a unanimous “coverup.” We show that in this case the set of payoffs that are sustainable in equilibrium coincides with the weakly renegotiation proof payoffs of the standard repeated game. Copyright Springer-Verlag Berlin/Heidelberg 2005