Abstract: This chapter introduces the adverse-selection approach to reputations. The chapter considers a long-lived player facing a sequence of short-lived players. If there is some (perhaps very small) chance that the long-lived players is a commitment (or action) type, then the payoff for a sufficiently patient long-lived player (in any Nash equilibrium of the repeated game) must be close to the payoff he would receive if he was known to be that commitment type (the Stackelberg payoff). This result is established for perfect monitoring games using arguments based on Bayes’ rule and for imperfect monitoring games using martingale arguments (merging). A characterization of asymptotic play shows that for imperfect monitoring games, reputations are temporary.

Keywords: action type, adverse selection, commitment type, merging, payoff bound, reputation, short-lived players, Stackelberg payoff, temporary reputations,