Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method

Kaisheng Liu,Yumei Xing

doi:10.3390/math7050469

Abstract

In this article, we introduce a model of bi-matrix games based on crisp parametric payoffs via utilizing the method of interval value function. Then, we get that equilibrium solutions of bi-matrix games on the basis of fuzzy payoffs and equilibrium solutions of the game model are of equal value. Furthermore, it is concluded that equilibrium solutions of the game can be converted to optimal solutions of discrete nonlinear optimization problems with parameters. Lastly, the proposed methodology is illustrated by an example.

Highlights

In various areas of the real world, the relations between the interests of two players are very complex, because matrix game has some limitations in practical applications
On the basis of [5,6,8], we will introduce a non-linear optimization method for a model of bi-matrix games based on crisp parametric payoffs by making use of the method of interval value function in this article
This article has presented a model of bi-matrix game ( BGIVFP) based on crisp parametric payoffs via making use of the method of interval value function

Summary

Introduction

In various areas of the real world, the relations between the interests of two players are very complex, because matrix game has some limitations in practical applications. A model of interval bi-matrix games is discussed by Hladik [15] They obtained the conclusion that solutions of this model are equal to optimal solutions of crisp nonlinear optimization problems based on parameters. Whereafter, through utilizing bilinear programming method and defuzzification ranking method, Li [8] solved the model of bi-matrix game based on payoffs in the context of intuitionistic fuzzy numbers. On the basis of [5,6,8], we will introduce a non-linear optimization method for a model of bi-matrix games based on crisp parametric payoffs by making use of the method of interval value function in this article.

Preliminaries

Example

Conclusions