Games in possibility capacities with payoff expressed by fuzzy integral

Abstract

This paper studies non-cooperative games where players are allowed to play their mixed non-additive strategies. Expected payoffs are expressed by so-called fuzzy integrals: Choquet integral, Sugeno integral and generalizations of Sugeno integral obtained by using triangular norms. We consider the existence problem of Nash equilibrium for such games. Positive results for Sugeno integral and its generalizations are obtained. However we provide some example of a game with Choquet payoffs which have no Nash equilibrium. Such example demonstrates that fuzzy integrals based on the maximum operation are more suitable for possibility capacities then Choquet integral which is based on the addition operation.