A Linear Programming Approach to Solve Constrained Bi-matrix Games with Intuitionistic Fuzzy Payoffs

Abstract

In many real games, two players’ payoffs are not exactly opposite and players often have some constraints or preference on their strategies. Such kinds of games are called constrained bi-matrix games (CBGs) for short. Based on dual programming theory, two linear programming models are developed for solving any CBG. Then, a classic example of bi-matrix games called the Rock-scissors-cloth game with considering players’ preference on strategies is used to show the validity of the proposed models and method. Furthermore, we investigate on the CBGs with payoffs represented by intuitionistic fuzzy numbers, which are simply called intuitionistic fuzzy CBGs in which both the ambiguity of the payoffs and the constraints of the strategies are taken into account. At last, the effectiveness of the proposed models and method is demonstrated with a numerical example of the company development strategy choice problem.