This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information.

This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information.

under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in bounded-recall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure...

In an experiment on the repeated prisoner's dilemma where intended actions are implemented with noise, Fudenberg et al. (2012) observe that non-equilibrium strategies of the "tit-for-tat" family are largely adopted. Furthermore, they do not find support for risk dominance of TFT as a determinant...

We study repeated games with imperfect public monitoring and unequal discounting. We characterize the limit set of perfect and public equilibrium payoffs as discount factors converge to 1 with the relative patience between players fixed. We show that the pairwise and individual full rank...

We consider a two-player Prisoner's Dilemma type game with continuous actions, where players choose how much to contribute to a public project. This game is played infinitely many times and actions are irreversible: players cannot decrease their actions over time. While it is strictly dominant...

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stage-game actions of player two imperfectly, while player two monitors the pure stage-game actions of player one perfectly. Player one's type is...

Flexibility - the ability to react swiftly to others' choices - facilitates collusion by reducing gains from defection before opponents react. Under imperfect monitoring, however, flexibility may also hinder collusion by inducing punishment after too few noisy signals. The combination of these...

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stage- game actions of player two imperfectly, while player two monitors the pure stage- game actions of player one perfectly. Player one’s type is...

Many markets without repeated seller–buyer relations feature third-party “monitors” that sell recommendations. We analyze the profit-maximizing recommendation policies of such monitors. In an infinitely repeated game with seller moral hazard and short-lived consumers, a monopolistic...