  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.
