We consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the...

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

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 ε -equilibria for all ε 0. We show by examples that there are: 1. quasiconcave, payoff secure...

We characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of (; ) equilibrium in which the fraction of players not optimizing is less than we show that a strategy is a Nash equilibrium in a...

We consider an asymptotic version of Mas-Colell's theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players' payoff functions are selected from an equicontinuous family, then all sufficiently large games have an pure, equilibrium for all gt; 0....

We show that for any discount factor, there is a natural number M such that all subgame perfect equilibrium outcomes of the discounted repeated prisoners' dilemma can be obtained by subgame perfect equilibrium strategies with the following property: current play depends only on the number of the...