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A Novel Algorithm For Finding Equilibrium Strategy In Two Person Zero Sum Game With Fuzzy Strategy Sets And Payoffs

Seyyed Mohammad Reza Farshchi, Gelare Veisi, Taghi Karimi, Morteza Aghaei
2011 Journal of Mathematics and Computer Science  
This paper investigates a two person zero sum matrix game in which the payoffs and strategy are characterized as random fuzzy variables.  ...  Based on random fuzzy expected value operator, a random fuzzy expected minimax equilibrium strategy to the game is defined.  ...  Two Person Zero Sum Matrix Game In this section, we discuss a two person zero sum matrix game in which the payoffs are characterized as fuzzy random variables, and then we define a fuzzy random expected  ... 
doi:10.22436/jmcs.02.04.02 fatcat:zw4h5ecuibfupe74l377e4hocy

A method to solve two-player zero-sum matrix games in chaotic environment

Hamiden Abd El- Wahed Khalifa, Pavan Kumar
2021 Independent Journal of Management & Production  
This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment.  ...  In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix.  ...  It was demonstrated that a two-person zero-sum matrix game with fuzzy payoffs and goals is equivalent to two linear programming problems (LPPs) (Bector, Chandra & Vijay, 2004 , 2004a .  ... 
doi:10.14807/ijmp.v12i1.1295 fatcat:qdmvrvujcfb2jkcs3s5bmutqnq

Nash equilibrium strategy for fuzzy non-cooperative games

Li Cunlin, Zhang Qiang
2011 Fuzzy sets and systems (Print)  
In this article, two-person zero-sum games are investigated in the fuzzy environment.  ...  In order to investigate the existence of (weak) Pareto Nash equilibrium strategies for fuzzy matrix games, we introduce the concept of crisp bi-matrix games with parameters.  ...  Theorem 3. 8 . 8 Let˜ be two-person zero-sum games with fuzzy payoffs.  ... 
doi:10.1016/j.fss.2011.03.015 fatcat:hsn7ekm5rjd7vlv7cgv6lngs74

Characterization of Nash Equilibrium Strategy for Heptagonal Fuzzy Games

2018 International Journal of Analysis and Applications  
In this paper, the Nash equilibrium strategy of two-person zero-sum games with heptagonal fuzzy payoffs is considered and the existence of Nash equilibrium strategy is studied.  ...  Also, based on the fuzzy max order several models in heptagonal fuzzy environment is constructed and the existence of their equilibrium strategies is proposed.  ...  Two-person Zero-sum Matrix Fuzzy Games In this section, we shall consider two-person zero-sum games with fuzzy payoffs.  ... 
doi:10.28924/2291-8639-16-2018-353 fatcat:5uqeecg5vvdmxczd32kdfhszhq

Page 4676 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
This paper considers a special class of zero-sum two-person games with noncontinuous payoff functions. This class contains the gen- eral games of timing as a subclass.  ...  In the paper some bilateral sequential non-zero-sum two person games are considered.  ... 

Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games

Hitoshi Yano, Ichiro Nishizaki
2016 Applied Mathematics  
In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs.  ...  most disadvantage strategy for the self.  ...  They also investigated the equilibrium solutions in two-person non-zero-sum games with fuzzy goals and vector fuzzy payoffs.  ... 
doi:10.4236/am.2016.75036 fatcat:s7lamu55xfaglhgab3yyjegpoa

A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs

Jiuping Xu, Liming Yao
2010 International Journal of Mathematics and Mathematical Sciences  
We concentrate on discussing a class of two-person zero-sum games with rough payoffs.  ...  Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy andr-trust maximin equilibrium strategy are defined.  ...  Acknowledgments This research has been supported by the Key Program of NSFC Grant no. 70831005 and the National Science Foundation for Distinguished Young Scholars, China Grant no. 70425005 .  ... 
doi:10.1155/2010/404792 fatcat:b6cj75wah5dyzcahurzshtzbpu

A Fictitious Play Algorithm for Matrix Games with Fuzzy Payoffs

Emrah Akyar
2012 Abstract and Applied Analysis  
Fuzzy matrix games, specifically two-person zero-sum games with fuzzy payoffs, are considered.  ...  In view of the parametric fuzzy max order relation, a fictitious play algorithm for finding the value of the game is presented.  ...  Two-Person Zero-Sum Game with Fuzzy Payoffs and Its Equilibrium Strategy In this section, we consider zero-sum games with fuzzy payoffs with two players, and we assume that player I tries to maximize the  ... 
doi:10.1155/2012/950482 fatcat:skfepch2drgqhlbbiaaoojn2qq

Two-Person Non Zero-Sum Bimatrix Game with Fuzzy Payoffs and Its Equilibrium Strategy

Chunyan Han, Zuofeng Gao, Yongbo Yu, Hua Zhang, Suting Zhang, Hongxin Bai
2009 Journal of Mathematics Research  
In this paper, we consider fuzzy bimatrix games with fuzzy payoffs. Based on fuzzy max order, for such games, we define three kinds of concepts of minim ax equilibrium strategies.  ...  Two-person zero-sum game with fuzzy payoffs and its equilibrium strategy Let I, J denote players and let M = {1, 2, · · · , m}, N = {1, 2, · · · , n} be the sets of all pure strategies available for player  ...  two-person zero-sum games with crisp payoffs Γ 1 =< {I, J}, X, Y, A L 0 , B L 0 > , Γ 2 =< {I, J}, X, Y, A R 0 , B R 0 >.  ... 
doi:10.5539/jmr.v1n1p57 fatcat:hmccvijnqfduzcpfaivnmprdui

Page 7227 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
M.S. (6-POND; Pondicherry) Fuzzy games. (English summary) J. Fuzzy Math. 10 (2002), no. 4, 817-829. The paper deals with the fuzzification of two-player zero-sum games having no saddle points.  ...  It is also shown that in games with a fixed order of moves the guaranteed best results of the players coincide and in zero sum games the highest guaranteed pay-off of a player is equal to the smallest  ... 

A Two Person Zero Sum Game Oriented to Integration of Objectives

Hakan Aplak, Mehmet Kabak, Erkan Köse
2014 Journal of Military Studies  
In this study, a two-person zero-sum game approach is presented for choosing optimal strategies of actors in competitive environment by balancing objectives reciprocally.  ...  Game theory is an approach based on mathematics in which strategies of players are evaluated reciprocally by considering environmental effects.  ...  Two-person zero-sum game approach is used to find optimal strategies of actors by balancing objectives reciprocally.  ... 
doi:10.1515/jms-2016-0190 fatcat:kpnb76xm3zf5xd5uwb7vbgowa4

Page 5279 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
Summary: “We prove that if all the off-diagonal entries of the payoff matrix of a finite symmetric two-player zero-sum game are odd integers then there exists a unique equilibrium in mixed strategies.”  ...  The author describes Nash equilibria for a 2-person, non-zero- sum (duel) game of timing in which the termination time is a discrete random variable taking one of two possible values, each with probability  ... 

Solutions for fuzzy matrix games

Adem C. Cevikel, Mehmet Ahlatçıoğlu
2010 Computers and Mathematics with Applications  
In this paper, we deal with two-person zero-sum games with fuzzy payoffs and fuzzy goals.  ...  We have presented two models for studying two-person zero-sum matrix games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs.  ...  Introduction In this work, we consider two-person zero-sum games with fuzzy payoffs and fuzzy goals. A payoff matrix with elements is represented as a fuzzy payoff matrix.  ... 
doi:10.1016/j.camwa.2010.04.020 fatcat:3kdb7gih7rf7fblfi5ogsx73ei

Page 3928 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
For the Cournot oligopoly game, conditions are given for the equilibrium point to exist and to be unique. Similar results are obtained for the special case of two-person zero-sum games.  ...  Non-cooperative n-person games with continuous payoff functions and real lines as players’ strategy sets are considered.  ... 

Page 1782 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
(PL-WROCT; Wroclaw) Nash equilibria of discontinuous non-zero-sum two-person games.  ...  For two-person zero-sum games, the existence of value and station- ary optimal strategies for both players is established by imposing Lyapunov-type stability assumptions.  ... 
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