Abstract
The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called TrIFN bimatrix games for short. In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation. Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games. It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.
Highlights
Bimatrix games are an important type of two-person nonzero-sum noncooperative games, which have been successfully applied to many different areas such as politics, economics, and management
The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called Trapezoidal intuitionistic fuzzy numbers (TrIFNs) bimatrix games for short
We model TrIFN bimatrix games and develop the parametric bilinear programming models and method by using the new order relation of TrIFNs given in this paper
Summary
Bimatrix games are an important type of two-person nonzero-sum noncooperative games, which have been successfully applied to many different areas such as politics, economics, and management. Larbani [5] proposed an approach to solving fuzzy bimatrix games based on the idea of introducing “nature” as a player in fuzzy multiattribute decision-making problems. Based on the concept of value index and ambiguity index, we propose a difference-index based ranking method of TrIFNs in this paper. This ranking method has good properties such as the linearity. A TrIFN bimatrix game is formulated and a solution method is developed on the difference-index based ranking bilinear programming.
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