A note on rationalizability and reputation with two long-run players

This note shows how a patient player in a two-person repeated game can build a reputation and achieve his stage-game Stackelberg payoff, provided that his opponent is rational and assigns positive prior probability to the committment type the patient player wants to imitate. This result is proposed as an illustration of a general approach to the analysis of incomplete information games, whereby simple and transparent assumptions about players' rationality and beliefs replace the traditional Bayesian-Nash equilibrium cum common prior hypothesis.