We present a purification result for incomplete information games with a large but finite number of players that allows compact metric spaces for both actions and types. We then compare our framework and findings to the early purification theorems of Rashid (1983. Equilibrium points of...

We show that a distribution of a game with a continuum of players is an equilibrium distribution if and only if there exists a sequence of symmetric approximate equilibrium distributions of games with fi- nite support that converges to it. Thus, although not all games have symmetric equilibrium...

Over the years, several formalizations of games with a continuum of players have been given. These include those of Schmeidler (1973), Mas-Colell (1984) and Khan and Sun (1999). Unlike the others, Khan and Sun (1999) also addressed the equilibrium problem of large ¯- nite games, establishing...

We show that every bounded, continuous at infinity game of perfect information has an "!perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing form the...

We study whether we can weaken the conditions given in Reny [4] and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy "!equilibria for all " 0. We show by examples that there are: 1. quasiconcave, payoff secure...

We consider Salim Rashids asymptotic version of David Schmeidlers theorem on the purification of Nash equilibria. We show that, in contrast to what is stated, players payoff functions have to be selected from an equicontinuous family in order for Rashids theorem to hold. That is, a bound on the...

The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship...