Frequent Monitoring in Repeated Games under Brownian Uncertainty

Abstract

This paper studies frequent monitoring in a simple in…nitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length. It shows that e ¢ cient strongly symmetric perfect public equilibrium payo¤s can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e.! 0. The approach proposed places distinct initial conditions on the process, which depend on the unknown action pro…le simultaneously and privately decided by the players at the beginning of each period of the game. The strong decreasing e¤ect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit. The existence of a positive monotonic relation between payo¤s and monitoring intensity is also found