Equilibrium under uncertainty with Sugeno payoff

This paper studies n-player games where players' beliefs about their opponents' behavior are capacities (fuzzy measures, non-additive probabilities). The concept of an equilibrium under uncertainty was introduced by J. Dow and S. Werlang [5] for two players and was extended to n-player games by J. Eichberger and D. Kelsey [8]. Expected utility was expressed by Choquet integral. We consider the concept of an equilibrium under uncertainty in this paper but with expected utility expressed by Sugeno integral. Existence of such an equilibrium expressed by possibility (or necessity) capacities is demonstrated using some abstract non-linear convexity on the space of capacities.