Abstract
The aim of this paper is to develop an effective method for solving bimatrix games with payoffs of intuitionistic fuzzy value. Firstly, bimatrix game model with intuitionistic fuzzy payoffs (IFPBiG) was put forward. Secondly, two kinds of nonlinear programming algorithms were discussed with the Nash equilibrium of IFPBiG. Thirdly, Nash equilibrium of the algorithm was proved by the fixed point theory and the algorithm was simplified by linear programming methods. Finally, an example was solved through Matlab; it showed the validity, applicability, and superiority.
Highlights
Since the 1940s, game theory [1, 2] has been developed to descript, analyze, and solve the duels among a group of rational agents with strategical behavior
The aim of this paper is to develop an effective method for solving bimatrix games with payoffs of intuitionistic fuzzy value
Matrix games have been extensively studied [3–23] and successfully applied to some fields [24–27]. It is becoming an important research field which can be classified into cooperative games and noncooperative games, zero sum games and nonzero sum games, and crisp matrix games and fuzzy matrix games
Summary
The aim of this paper is to develop an effective method for solving bimatrix games with payoffs of intuitionistic fuzzy value. Bimatrix game model with intuitionistic fuzzy payoffs (IFPBiG) was put forward. Two kinds of nonlinear programming algorithms were discussed with the Nash equilibrium of IFPBiG. Nash equilibrium of the algorithm was proved by the fixed point theory and the algorithm was simplified by linear programming methods. An example was solved through Matlab; it showed the validity, applicability, and superiority
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