Equilibrium under uncertainty with Sugeno payoff

TL;DR

This paper extends the concept of equilibrium under uncertainty to n-player games by using Sugeno integrals for expected utility, demonstrating existence through non-linear convexity methods.

Contribution

It introduces a new equilibrium concept under uncertainty with Sugeno integrals and proves its existence using abstract non-linear convexity techniques.

Findings

Existence of equilibrium under uncertainty with Sugeno integrals established.

Generalizes previous models using Choquet integrals to Sugeno integrals.

Provides a mathematical framework for capacities with non-linear convexity.

Abstract

This paper studies n-player games where players beliefs about their opponents behaviour are capacities. The concept of an equilibrium under uncertainty was introduced J.Dow and S.Werlang (J Econ. Theory 64 (1994) 205--224) for two players and was extended to n-player games by J.Eichberger and D.Kelsey (Games Econ. Behav. 30 (2000) 183--215). 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 is demonstrated using some abstract non-linear convexity on the space of capacities.