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This paper studies non-cooperative games where players are allowed to playtheir mixed non-additive strategies. Expected payoffs are expressed byso-called fuzzy integrals: Choquet integral, Sugeno integral andgeneralizations of Sugeno integral obtained by using triangular norms. Weconsider the existence problem of Nash equilibrium for such games. Positiveresults for Sugeno integral and its generalizations are obtained. However weprovide some example of a game with Choquet payoffs which have no Nashequilibrium. Such example demonstrates that fuzzy integrals based on themaximum operation are more suitable for possibility capacities then Choquetintegral which is based on the addition operation.

Games in possibility capacities with payoff expressed by fuzzy integral