A new characterization of perfect public equilibrium payoffs in repeated games with imperfect public monitoring in continuous time∗

This paper continues the study of a new class of repeated games with imperfect public monitoring launched by Sannikov (2007). I provide a new characterization of self-generating sets for a class of games in continuous time and Brownian information. This new characterization relies on partial differential equation techniques. Our approach gives a geometric characterization of the set of perfect public equilibrium payoffs, similar to the 2-player characterization obtained by Sannikov (2007) who obtains a curvature relation through a direct argument. Our characterization via partial differential equations is obtained by first identifying self-generating sets as stochastically viable under the dynamic determining the continuation payoff process induced by the players’ strategies. Based on this formal identification we use viscosity solution techniques to derive a geometric characterization of the boundary of self-generating sets. In case of two players my characterization reduces to the result reported by Sannikov (2007), relating the curvature parameters of a set to incentives.