In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players' information for the purposes of determining a player's behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential...

We investigate a common-value labor setting in which firms interview a worker prior to hiring. When firms have private information about the worker’s value and interview decisions are kept private, many firms may enter the market, interview, and hire with positive probability. When firms’...

We study optimal price discrimination when a monopolist faces a continuum of consumers with reference-dependent preferences. A consumer's valuation for product quality consists of an intrinsic valuation affected by a private state signal (type), and a gain-loss valuation that depends on...

A population of players of players is randomly matched to play a normal form game G. The payoffs in this game represent the fitness associated with the various outcomes. Each individual has preferences over the outcomes in the game and chooses an optimal action with respect to those preferences....

We prove the folk theorem for the Prisoner's dilemma using strategies that are robust to private monitoring. From this follows a limit folk theorem: when players are patient and monitoring is sufficiently accurate, (but private and possibly independent) any feasible individually rational payoff...

In repeated games, simple strategies such as Grim Trigger, while strict equilibria when monitoring is perfect, can fail to be even approximate Nash equilibria when monitoring is private, yet arbitrarily close to perfect. That is, they fail to be robust to private monitoring. In this paper, it is...