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.

Applying unawareness belief structures introduced in Heifetz, Meier, and Schipper (2013a), we develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower...

This article provides a brief survey of the literature on unawareness and introduces the contributions to the special issue on unawareness in Mathematical Social Sciences. First, we provide a brief overview both about epistemic models of unawareness and models of extensive-form games with...

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are...

In this paper we formulate a solution concept without making assumptions about expected utility maximization, common knowledge or beliefs. Beliefs, strate- gies and the degree to which players are expected utility maximizers are endoge- nously determined as part of the solution. To achieve this,...

We consider consumers with the same reservation price, who desire to buy at most one unit of a good. Firms compete only in prices but there are other features firms cannot control that would eventually lead an agent to buy in one firm or another. We introduce such uncertainty in a model of a...

This paper extends Savage's subjective approach to probability and utility from decision problems under exogenous uncertainty to choice in strategic environments. Interactive uncertainty is modeled both explicitly, using hierarchies of preference relations, the analogue of beliefs hierarchies,...

Purification results are important in game theory and statistical decision theory. The purpose of this paper is to prove a general purification theorem that generalizes many authors' results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show...

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are...

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are...