Existence of almost fixed points for random operators with application in game theory

Abstract

We introduce the notion of the random epsilon-fixed point for random operators. Then we prove some existence theorems in order to apply this results in game theory for example we will prove existence of epsilon-random Nash equilibrium in some class of random games. Such games can be applied in the environment in which Bayesian equilibria are considered, i.e. in games in which payoffs of players are known up to dependence on assignment of the players to specific types.