Abstract
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. In the sequel, the existence of Pareto Nash equilibrium strategies and weak Pareto Nash equilibrium strategies is investigated for fuzzy matrix games. Finally, the relation between Pareto Nash equilibrium strategy and parametric bi-matrix games is established.
Highlights
Modern game theory was developed by the mathematician John Von Neumann in the Mid-1940‘s and in 1944, he published the book of ”Theory of games and economic behavior” joint with Morgenstern [9]
The existence of Pareto Nash equilibrium strategies and weak Pareto Nash equilibrium strategies is investigated for fuzzy matrix games
In this article we focus on a class of non-cooperative games namely two-person zero-sum matrix games
Summary
Modern game theory was developed by the mathematician John Von Neumann in the Mid-1940‘s and in 1944, he published the book of ”Theory of games and economic behavior” joint with Morgenstern [9]. Zero-sum matrix game; fuzzy payoffs; Nash equilibrium; heptagonal fuzzy number. In 2011, Cunlin and Zhang Qiang [4] investigated two-person zero-sum games in the symmetric triangular fuzzy environment. They obtained Nash equilibrium of two-person zero-sum games with fuzzy payoff. In this paper we define the k-heptagonal fuzzy numbers and generalize Cunlin and Qiang [4] and Bapi Dutta [3] Nash equilibrium solution concepts.
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