This chapter studies the theory of value of games with infinitely many players.Games with infinitely many players are models of interactions with many players. Often most of the players are individually insignificant, and are effective in the game only via coalitions. At the same time there may...

In interactive contexts such as games and economies, it is important to take account not only of what the players believe about substantive matters (such as payoffs), but also of what they believe about the beliefs of other players. Two different but equivalent ways of dealing with this matter,...

Perfectly competitive economies are economic models with many agents, each of whom is relatively insignificant. This chapter studies the relations between the basic economic concept of competitive (or Walrasian) equilibrium, and the game-theoretic solution concept of value. It includes the...

In this article, we consider how important developments in game theory have contributed to the theory of industrial organization. Our goal is not to survey the theory of industrial organization; rather, we consider the contribution of game theory through a careful discussion of a small number of...

In this survey article, we report results on the existence of pure-strategy Nash equilibria in games with an atomless continuum of players, each with an action set that is not necessarily finite. We also discuss purification and symmetrization of mixed-strategy Nash equilibria, and settings in...

This chapter surveys a class of solution concepts for n-person games without transferable utility -- NTU games for short -- that are based on varying notions of "fair division". An NTU game is a specification of payoffs attainable by members of each coalition through some joint course of action....