Unattainable Payoffs for Repeated Games of Private Monitoring

We bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. Our approach treats 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. This quantifies the dynamic strategic effect of correlation. 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. This bound can be made tight with a simple two-stage procedure. The techniques we develop are tractable and apply to many important economic settings such as dynamic oligopoly, long-term partnerships, and relational contracting. In all cases, they provide the sharpest possible equilibrium payoff prediction that is agnostic about the monitoring structure