Equilibrium under uncertainty with fuzzy payoff

TL;DR

This paper introduces a new equilibrium concept in n-player games where players' beliefs are modeled by fuzzy measures, using a fuzzy integral based on continuous t-norms, extending previous models with Sugeno and Choquet integrals.

Contribution

It generalizes the equilibrium under uncertainty framework by employing fuzzy integrals generated by continuous t-norms, broadening the scope of belief modeling in game theory.

Findings

Develops a new equilibrium concept using fuzzy integrals with t-norms.

Extends previous models by incorporating a more general fuzzy integral.

Provides theoretical foundations for equilibrium analysis under fuzzy beliefs.

Abstract

This paper studies n-player games where players beliefs about their opponents behaviour are capacities (fuzzy measures, non-additive probabilities). 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). Expected utility (payoff function) was expressed by Choquet integral. The concept of an equilibrium under uncertainty with expected utility expressed by Sugeno integral were considered by T.Radul (2018). We consider in this paper an equilibrium with expected utility expressed by fuzzy integral generated by a continuous t-norm which is a natural generalization of Sugeno integral.