Mediated subgame perfect equilibrium

Abstract

This paper studies mediation in infinitely repeated games with perfect monitoring. In departure from the literature, we assume that all private messages and internal records are publicly revealed at the end of each stage. We call the resulting equilibrium concept mediated subgame perfect equilibrium (MSPE). It is shown that the revelation principle holds. We introduce an effective correlated minimax value, which can be conveniently determined as the solution of a linear program, and use it to derive necessary and sufficient conditions for the implementability of payoffs under an MSPE. These conditions are standard for two-player games with a sufficient degree of patience but are, in general, strictly more permissive. Examples illustrate the impact of effective correlated minimax profiles and the subtle role of internal records.