Fuzzy Constrained Matrix Games And Fuzzy Bimatrix Games

In game theory, matrix game becomes a research focus and has received a generous concern. The most studied problem in matrix game is the games with fuzzy strategy and crisp payoffs or the games with crisp strategy and fuzzy payoffs or the games with fuzzy strategy and fuzzy payoffs. As an emerging branch of game theory, fuzzy game theory has attracted many scholars'interest since the last 70's, some research results appeared one after another. The purpose of this paper is to revising and perfecting the mature theories of crisp matrix game and bimatirx game. It affords theoretic bases for solving matrix game.In crisp matrix game and bimatrix game model, many scholars considered the value and equilibrium strategy of matrix game and bimatrix game with fuzzy payoffs. In fact due to the objective environment, players has some restrictions when they chosen strategies. The paper introduces matrix game with interval payoffs; considers matrix game with constrained strategies and fuzzy payoffs to make the players more in line with the actual when they choose strategies; then we defines three kinds of concepts of minimax equilibrium strategies to fuzzy bimatirx game, it promoted the development of the bimatrix games.The paper can be divided into four chapters. First chapter is introduction, it provides development histories of classical games theory, background and practical value of the paper. In the second part we introduce some basic concepts and definitions of crisp matrix games and two-person zero-sum matrix games with internal data. In chapter three we introduce the dual linear programming theory with fuzzy parameters, link the fuzzy matrix game with dual linear programming theory, and give the methods to solve the game. In the last part of the paper we give the method of solving fuzzy bimatirx game with quadratic programming problem; define three kinds of concepts of minimax equilibrium strategies to fuzzy bimatrix game and give the relations of fuzzy bimatrix game and parametric bimatrix game.