Economic Theory: Steady-State Equilibria in Anonymous Repeated Games, I: Trigger Strategies in General Stage Games

Abstract

We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. We then focus on “trigger-strategy” equilibria. When the updating of a player’s record can depend on the actions of both players in a match, steady-state equilibria in trigger strategies can support the play of a wide range of actions, including any action that Pareto-dominates a static Nash equilibrium. When updates can depend only on a player’s own actions, fewer actions can be supported by steady-state equilibria. We provide sufficient conditions for trigger equilibria to support a given action, along with somewhat more permissive necessary conditions. When players have access to a form of decentralized public randomization, the sufficient conditions expand to match the necessary conditions.
joint with Daniel Clark and Drew Fudenberg