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 article gives a brief introduction to reputation effects. A canonical model is described, the reputation bound result of Fudenberg and Levine (1989 1992) and the temporary reputation result of Cripps, Mailath, and Samuelson (2004, 2007) are stated and discussed.

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 note characterizes the set A¡∞ of actions of player ¡ that are uniquely rationalizable for some hierarchy of beliefs on an arbitrary space of uncertainty. It is proved that for any rationalizable action a¡ for the type t¡, if a¡ belongs to A¡∞ and is justified by conjectures...

We showed in McLean and Postlewaite (2014) that when agents are informationally small, there exist small modifications to VCG mechanisms in interdependent value problems that restore incentive compatibility. This paper presents a two-stage mechanism that similarly restores incentive...

In repeated normal-form (simultaneous-move) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. By means of examples, we identify two types of...

I develop a set-theoretic model of unawareness without making any structural assumptions on the underlying state space. Unawareness is characterized as a measurability constraint that results in players' reasoning about a “coarse" subjective algebra of events. The model is shown to be...

I construct a state space model with unawareness following Aumann (1976). Dekel, Lipman and Rustichini (1998a) show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that...

We develop an auction model for the case of interdependent values and multidimensional signals in which agents’ signals are correlated. We provide conditions under which a modification of the Vickrey auction which includes payments to the bidders will result in an ex post efficient outcome....

This paper extends Li (2008b) to the multi-agent environment, where players reason about each other’s awareness as well as knowledge, subject to their own awareness constraints. I characterize the interactive knowledge hierarchies under unawareness, which significantly differ from those in the...