Tit-For-Tat Equilibria in Discounted Repeated Games with Private Monitoring

We investigate infinitely repeated games with imperfect private monitoring. We focus on a class of games where the payoff functions are additively separable and the signal for monitoring a player's action does not depend on the other player's action. Tit-for-tat strategies function very well in this class, according to which each player's action in each period depends only on the signal for the opponent's action one period before. With almost perfect monitoring, we show that even if the discount factors are fixed low, efficiency is approximated by a tit-for-tat Nash equilibrium payoff vector.