A new kind of equilibrium in dynamic games with beliefs

We shall introduce a new notion of equilibrium -- belief-distorted Nash equilibrium (BDNE) -- in discrete time dynamic games in which players do not have perfect information about strategies chosen by the other players and form some expectations about them. A game in the strategic form is generally a triple of objects: the set of players (with, possibly, some structure imposed), their strategy sets and payoff functions defined on the set of profiles of strategies.The usual concept of Nash equilibrium requires that at an equilibrium profile every player (almost every in the case of infinitely many players represented as a measure space) maximizes his payoff as the function of his strategy given the strategies of the remaining players. In the concepts of belief-distorted Nash equilibrium we assume that at each stage of the game players maximize another functions related both to the original payoff functions and players' beliefs about future behaviour of the system. Various notions of self- verification are introduced. Equivalence between a BDNE for perfect foresight beliefs and Nash equilibrium is proven. The concepts are illustrated by examples of exploitation of a common renewable resource and a repeated minority game.