Existence of nash equilibrium in atomless games

Abstract

In this thesis we first discuss games with private information. Based on our mathematical results on the set of distributions induced by the measurable selections of a correspondence with a countable range, we provide the purification results and also prove the existence of a pure strategy equilibrium for a finite game when the action space is countable but not necessarily compact.Another aspect of this thesis focuses on large games. We show the existence of equilibrium for a game with continuum of players that are divided into finite types, and with countable actions. Also, the existence of pure-strategy Nash equilibrium is shown for a non-cooperative game with a continuum of small players and a compact action space. The players' payoffs depend on their own actions and the mean of the transformed strategy profles. This covers the case when the payoffs depend on players own actions and fnitely many summary statistics.