A Novel Algorithm for Finding Equilibrium Strategy in Two Person Zero Sum Game with Fuzzy Strategy Sets and Payoffs

Volume 2, Issue 4, pp 580--587 http://dx.doi.org/10.22436/jmcs.02.04.02

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Authors

Seyyed Mohammad Reza Farshchi - Department of Artificial Intelligence, Islamic Azad University, Mashhad Branch Gelare Veisi - Department of Computer Engineering, Islamic Azad University, Mashhad Branch Taghi Karimi - Department of Mathematics, Payam Noor University, Fariman Branch Morteza Aghaei - Payam Noor University, Mashhad Branch

Abstract

This paper investigates a two person zero sum matrix game in which the payoffs and strategy are characterized as random fuzzy variables. Using the operations of triangular fuzzy numbers, the fuzzy payoffs for all synthetic outcomes are calculated. Based on random fuzzy expected value operator, a random fuzzy expected minimax equilibrium strategy to the game is defined. After that, based on the constraints, the feasible strategy string sets of the players for multi conflict situations are constructed. Then an iterative algorithm based on random fuzzy simulation is designed to seek the minimax equilibrium strategy. Using a linear ranking function, the aggregation model can be solved by transforming it into a crisp bimatrix game. Then, the fuzzy synthetic aggregation model is established and solved by transforming it into a crisp bimatrix game. Finally, a military example is provided to illustrate the practicality and effectively of the model.

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Keywords

• Fuzzy game theory
• two person game
• equilibrium strategy
• fuzzy payoff.

MSC

•  00A69
•  91A10
•  91A05
•  91Axx

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