Continuous Time Limits of Repeated Games with Imperfect Public Monitoring,” Review of Economic Dynamics

Abstract: In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players ’ actions. Recent research has focused on the case of “frequent monitoring, ” where the time interval between periods becomes small. Here we study a simple example of a commitment game with a long-run and short-run player in order to examine different specifications of how the signal distribution depends upon period length. We give a simple criterion for the existence of efficient equilibrium, and show that the efficiency of the equilibria that can be supported depends in an important way on the effect of the player’s actions on the variance of the signals, and whether extreme values of the signals are “bad news ” of “cheating ” behavior, or “good news ” of “cooperative ” behavior. 1 Financial support from NSF grants SES-03-1471 and SES-0426199 is gratefully acknowledged. We would like to thank Eduardo Faingold, Yuliy Sannikov, and Andrzej Skrzypacz for helpful conversations, and Satoru Takahashi for careful proofreading.