On the non-existence of reputation effects in two-person infinitely-repeated games

Consider a two-person infinitely-repeated game in which one player is either a normal rational type or a commitment type that authomatically plays a fixed repeated-game strategy When her true type is private information a rational type may want to develop a reputation as a commitment type by mimicking the commitment type's actions But the uninformed player anticipating the behavior of the rational type may try to screen out the rational type by choosing an action which gives the rational type a low payoff when she mimics the commitment type My main result shows that for comparably patient players if the prior probability that the player is a commitment type is sufficiently small the screening process may take so long that the rational player does not benefit from developing a reputation In the case of equally patient players I show that the folk theorem holds even when both players possess a small amount of private information Schmidt (1994) and Cripps Schmidt and Thomas (1993) argue that reputation effects can rule out outcomes permitted by the folk theorem regardless of how small the prior probability that the player is a commitment type My results show that this argument only applies when one player is infinitely more patient than the other.