Unattainable Payoffs for Repeated Games of Private Monitoring

Abstract:     
We bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. The novelty in our approach is treating private histories as endogenous correlation devices. To do this, we develop a tractable new solution concept for standard repeated games with perfect monitoring: Markov Perfect Correlated Equilibrium generalizes the operator approach of Abreu, Pearce and Stacchetti (1990) in a natural way to allow for correlated strategies. We show that for any monitoring structure, the set of sequential equilibrium payoffs of the repeated private monitoring game is always contained within the set of Markov Perfect Correlated Equilibrium payoffs of the analogous repeated game. Further, we explore two senses in which this bound is tight.

Keywords: Repeated Games, Private Monitoring, Correlated Equilibrium

JEL Classifications: C7

Working Paper Series