Towards a Belief-Based Theory of Repeated Games with Private Monitoring: An Application of POMDP∗

An equilibrium in a repeated game with imperfect private moitoring is called a finite state equilibrium, if each player’s action on the equilibrium path is given by an automaton with a finite number of states. We provide a tractable general method to check the equilibrium conditions in this class. Our method is based on the belief-based approach and employs the theory of POMDP (Partially Observable Markov Decision Processes). This encompasses the majority of existing works.