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Keywords = fuzzy bi-matrix games

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10 pages, 272 KB  
Article
Impact of Risk Aversion in Fuzzy Bimatrix Games
by Chuanyang Xu, Wanting Zhao and Zhongwei Feng
Axioms 2024, 13(7), 469; https://doi.org/10.3390/axioms13070469 - 11 Jul 2024
Viewed by 1204
Abstract
In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, [...] Read more.
In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, β)-RANE and a mixed-strategy Nash equilibrium (MSNE) in a bimatrix game with a risk-averse player 2 and certain payoffs. Finally, considering 2 × 2 bimatrix games with STFPs, we find the conditions where the increase in player 2’s risk-aversion level hurts or benefits himself/herself. Full article
18 pages, 355 KB  
Article
Fuzzy Weighted Pareto–Nash Equilibria of Multi-Objective Bi-Matrix Games with Fuzzy Payoffs and Their Applications
by Wen Li, Deyi Li, Yuqiang Feng and Du Zou
Mathematics 2023, 11(20), 4266; https://doi.org/10.3390/math11204266 - 12 Oct 2023
Cited by 3 | Viewed by 1817
Abstract
Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has [...] Read more.
Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one Pareto–Nash equilibrium. Then, with the help of BGIP, we obtain the necessary and sufficient conditions for the existence of fuzzy Pareto–Nash equilibrium of MBGFP. Secondly, based on the bilinear programming method for calculating Nash equilibrium in crisp bi-matrix games, we established a bilinear programming method with parameters for calculating fuzzy Pareto–Nash equilibrium. By considering the importance of each objective to the players, MBGFP is transformed into a bi-matrix game with fuzzy payoffs (BGFP). Furthermore, we obtained the necessary and sufficient conditions for the existence of fuzzy weighted Pareto–Nash equilibrium and its calculation method. Finally, a practical example is used to illustrate the effectiveness of our proposed calculation method. Full article
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30 pages, 2878 KB  
Article
Bi-Matrix Games with General Intuitionistic Fuzzy Payoffs and Application in Corporate Environmental Behavior
by Shuying Li and Guoping Tu
Symmetry 2022, 14(4), 671; https://doi.org/10.3390/sym14040671 - 24 Mar 2022
Cited by 9 | Viewed by 2429
Abstract
Uncertainty is common in miscellaneous decision-making problems, including bi-matrix games. The uncertainty of bi-matrix games is caused by the complexity of the game environment and the limitations of players’ cognition rather than the asymmetry of information. Therefore, it is hard for players to [...] Read more.
Uncertainty is common in miscellaneous decision-making problems, including bi-matrix games. The uncertainty of bi-matrix games is caused by the complexity of the game environment and the limitations of players’ cognition rather than the asymmetry of information. Therefore, it is hard for players to precisely give their crisp payoff values. In this paper, a new method considering the acceptance degree that the general intuitionistic fuzzy constraints may be violated is developed to solve general intuitionistic fuzzy bi-matrix games (GIFBMGs). In the method, a new asymmetric general intuitionistic fuzzy number (GIFN) and its cut sets are firstly defined. Then, the order relationship of GIFNs and the definitions of α and β-bi-matrix games are proposed. Afterwards, the constructed general intuitionistic fuzzy quadratic program is converted into an interval bi-objective program on the basis of the order relationship of GIFNs. Furthermore, the interval bi-objective program is converted into a multi-objective quadratic program based on the combination of interval order relationship and the player’s acceptance degree. A goal programming approach is put forward to solve the multi-objective quadratic program. Finally, the validity of the proposed method is verified with a numerical example for corporate environmental behavior (CEB), and some comparative analyses are conducted to show the superiority of the proposed method. Full article
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10 pages, 251 KB  
Article
Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method
by Kaisheng Liu and Yumei Xing
Mathematics 2019, 7(5), 469; https://doi.org/10.3390/math7050469 - 24 May 2019
Cited by 4 | Viewed by 2919
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 [...] Read more.
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. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
15 pages, 276 KB  
Article
Multi-objective Fuzzy Bi-matrix Game Model: A Multicriteria Non-Linear Programming Approach
by Wei Zhang, Yumei Xing and Dong Qiu
Symmetry 2017, 9(8), 159; https://doi.org/10.3390/sym9080159 - 15 Aug 2017
Cited by 8 | Viewed by 4344
Abstract
A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results [...] Read more.
A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
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