Equilibrium under uncertainty with fuzzy payoff

Abstract

We study $n$-player games where players form non-additive beliefs about opponent's decisions and answer with pure strategies. The concept of an equilibrium under uncertainty was introduced by J. Dow and S. Werlang (1994) for two players and was extended to $n$-player games by J. Eichberger and D. Kelsey (2000). The authors consider payoff functions expressed by Choquet integral. The concept of an equilibrium under uncertainty with payoff functions expressed by the Sugeno integral were considered by T. Radul (2018). We consider a generalization of this result with payoff functions expressed by fuzzy integral generated by arbitrary continuous $t$-norm.