Toward a Theory of Discounted Repeated Games with Imperfect Monitoring

This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in external equilibria. We characterize these equilibria, and provide computational and comparative statics results. The “self-generation” and “bang-bang” propositions which were at the core of our analysis of optimal cartel equilibria [2], are generalized to asymmetric games and infinite action spaces. New results on optimal implicit reward functions include the necessity (as opposed to sufficiency) of bang-bang functions, and the nature of optimal punishment regions.