Unattainable Payoffs for Repeated Games of Private Monitoring

Abstract

We tightly bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. 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), but instead takes correlated equilibrium of the auxiliary game. We show that for any private monitoring structure, the set of sequential equilibrium payoffs of a repeated game is contained within the set of Markov Perfect Correlated Equilibrium payoffs of the repeated expected game. This bound can be made tight with a simple two-stage procedure. The techniques we develop are tractable and shed light on all economic settings with imperfectly observed actions, like dynamic oligopoly, long-term partnerships, and relational contracting. In all cases, they yield the sharpest equilibrium payoff prediction that is agnostic about the monitoring structure.