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

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

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. Fur...

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Bibliographic Details
Main Authors: Kaisheng Liu, Yumei Xing
Format: Article
Language:English
Published: MDPI AG 2019-05-01
Series:Mathematics
Subjects:
fuzzy bi-matrix games
equilibrium solutions
non-linear optimization problems
interval value function methods
Online Access:https://www.mdpi.com/2227-7390/7/5/469
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spelling doaj-8c7e48628ab8466d96b7f14e3a47433c2020-11-24T22:11:29ZengMDPI AGMathematics2227-73902019-05-017546910.3390/math7050469math7050469Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function MethodKaisheng Liu0Yumei Xing1School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaSchool of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaIn 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.https://www.mdpi.com/2227-7390/7/5/469fuzzy bi-matrix gamesequilibrium solutionsnon-linear optimization problemsinterval value function methods
collection DOAJ
language English
format Article
sources DOAJ
author Kaisheng Liu
Yumei Xing
spellingShingle Kaisheng Liu
Yumei Xing
Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
Mathematics
fuzzy bi-matrix games
equilibrium solutions
non-linear optimization problems
interval value function methods
author_facet Kaisheng Liu
Yumei Xing
author_sort Kaisheng Liu
title Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
title_short Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
title_full Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
title_fullStr Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
title_full_unstemmed Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
title_sort solving bi-matrix games based on fuzzy payoffs via utilizing the interval value function method
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-05-01
description 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.
topic fuzzy bi-matrix games
equilibrium solutions
non-linear optimization problems
interval value function methods
url https://www.mdpi.com/2227-7390/7/5/469
work_keys_str_mv AT kaishengliu solvingbimatrixgamesbasedonfuzzypayoffsviautilizingtheintervalvaluefunctionmethod
AT yumeixing solvingbimatrixgamesbasedonfuzzypayoffsviautilizingtheintervalvaluefunctionmethod
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