EAGT 2019: Game Theory pp 131-150

The Method for Solving Bi-matrix Games with Intuitionistic Fuzzy Set Payoffs

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1082)

Abstract

The aim of this paper is to develop a bilinear programming method for solving bi-matrix games in which the payoffs are expressed with intuitionistic fuzzy sets (IFSs), which are called IFS bi-matrix games for short. In this method, using the equivalent relation between IFSs and interval-valued fuzzy sets (IVFSs) and the operations of IVFSs, we propose a new order relation of IFSs through introducing a ranking function, which is proven to be a total order relation. Hereby we introduce the concepts of solutions of IFS bi-matrix games and parametric bi-matrix games. It is proven that any IFS bi-matrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bi-matrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The models and method proposed in this paper are demonstrated with a real example of the e-commerce retailers’ strategy choice problem.

Keywords

Noncooperative game Intuitionistic fuzzy set Bilinear programming Fuzzy game

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