Reputation and experimentation in repeated games with two long-run players

This paper considers reputation effects in a repeated game between two long-run players, one of whom is relatively patient and may be committed to a fixed strategy which punishes the opponent for increasingly long periods whenever inappropriate actions are taken. By following this commitment strategy, the more patient player can induce a sufficiently patient opponent to experiment to see whether the commitment strategy is also being followed off the equilibrium path. This can guarantee the more patient player (in any Nash equilibrium) a payoff close to the highest feasible payoff consistent with the individual rationality of the other player. For an arbitrary degree of patience of the less patient player a weaker result is established: the more patient player is guaranteed an average equilibrium payoff close to the static Stackelberg payoff. This latter result generalizes that of Schmidt (1993), who established the same result for the restricted class of games of conflicting interests.