Communication and Learning

We study the intergenerational accumulation of knowledge in an infinite-horizon model of communication. Each in a sequence of players receives an informative but imperfect signal of the once-and-for-all realization of an unobserved state. The state affects all players’ preferences over present and future decisions. Each player observes his own signal but does not directly observe the realized signals or actions of his predecessors. Instead, he must rely on cheap-talk messages from the previous players to fathom the past. Each player is therefore both a receiver of information with respect to his decision, and a sender with respect to all future decisions. Senders’ preferences are misaligned with those of future decision makers.

We ask whether there exist “full learning” equilibria — ones in which the players’ posterior beliefs eventually place full weight on the true state. We show that, regardless of how small the misalignment in preferences is, such equilibria do not exist. This is so both in the case of private communication in which each player only hears the message of his immediate predecessor, and in the case of public communication, in which each player hears the message of all previous players. Surprisingly, in the latter case full learning may be impossible even in the limit as all players become infinitely patient. We also consider the case where all players have access to a mediator who can work across time periods arbitrarily far apart. In this case full learning equilibria exist.