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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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 |
_version_ |
1725805394497896448 |