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A Novel Algorithm For Finding Equilibrium Strategy In Two Person Zero Sum Game With Fuzzy Strategy Sets And Payoffs
2011
Journal of Mathematics and Computer Science
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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
2021
Independent Journal of Management & Production
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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
2011
Fuzzy sets and systems (Print)
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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
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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
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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
2016
Applied Mathematics
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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
2010
International Journal of Mathematics and Mathematical Sciences
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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
2012
Abstract and Applied Analysis
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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
2009
Journal of Mathematics Research
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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
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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
2014
Journal of Military Studies
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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
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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
2010
Computers and Mathematics with Applications
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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
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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
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(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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