Evolutionary Stable Strategies in Games with Fuzzy Payoffs

TL;DR

This paper introduces a novel method for evaluating evolutionarily stable strategies in symmetric games with fuzzy payoffs, effectively handling uncertainty without information loss and establishing a relation with fuzzy Nash equilibria.

Contribution

It develops a fuzzy set-based approach to determine ESS in games with uncertain payoffs, avoiding defuzzification and incorporating fuzzy decision rules.

Findings

The method accurately characterizes fuzzy ESS in uncertain environments.

It maintains information integrity by avoiding defuzzification.

Numerical results confirm the approach as a valid generalization of ESS for fuzzy payoffs.

Abstract

Evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory. ESS provides an evolutionary stability criterion for biological, social and economical behaviors. In this paper, we develop a new approach to evaluate ESS in symmetric two player games with fuzzy payoffs. Particularly, every strategy is assigned a fuzzy membership that describes to what degree it is an ESS in presence of uncertainty. The fuzzy set of ESS characterize the nature of ESS. The proposed approach avoids loss of any information that happens by the defuzzification method in games and handles uncertainty of payoffs through all steps of finding an ESS. We use the satisfaction function to compare fuzzy payoffs, and adopts the fuzzy decision rule to obtain the membership function of the fuzzy set of ESS. The theorem shows the relation between fuzzy ESS and fuzzy Nash quilibrium. The numerical results illustrate the proposed method is an appropriate generalization of ESS to fuzzy payoff games.