Reputation and Experimentation in Repeated Games with Two Long-Run Players

The authors consider a repeated game between two long-run players, one of whom is relatively patient. Each player has a small amount of uncertainty about the other's strategy. Given a weak assumption about the support of this uncertainty, the more patient player obtains (in any Nash equilibrium) approximately the highest payoff consistent with the individual rationality of the other player, if the latter is patient enough. If the less patient player is relatively impatient, any Nash equilibrium gives the more patient player at least the Stackelberg payoff: this generalizes K. M. Schmidt's (1993) result, which applies only to games of conflicting interests.