Reputation with Analogical Reasoning∗

We consider a repeated interaction between a long-run player and a sequence of short-run players, in which the long-run player may either be rational or may be a mechanical type who plays the same (possibly mixed) action in every stage game. We depart from the classic model, exemplified by Fudenberg and Levine [4, 5], in assuming that the short-run players make inferences by analogical reasoning, meaning that they correctly identify the average strategy of each type of long-run player, but do not recognize how this play varies across histories. Concentrating on 2 × 2 games, we provide a complete characterization of equilibrium payoffs, establishing a payoff bound for the rational long-run player that can be strictly larger than the familiar “Stackelberg” bound. We also provide a complete characterization of equilibrium behavior, showing that play begins with either a reputation-building or (depending on parameters) a reputation-spending stage, followed by a reputation-manipulation stage. ∗We thank Olivier Compte, Drew Fudenberg, Rani Spiegler, and Asher Wolinsky for helpful discussions. Jehiel thanks the European Research Council for financial support. Samuelson thanks the National Science Foundation (SES-0850263) for financial support. Reputation with Analogical Reasoning