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2013 A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
Deng-Feng Li, Jie Yang
J. Appl. Math. 2013(SI08): 1-10 (2013). DOI: 10.1155/2013/697261

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.

Citation

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Deng-Feng Li. Jie Yang. "A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers." J. Appl. Math. 2013 (SI08) 1 - 10, 2013. https://doi.org/10.1155/2013/697261

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950825
MathSciNet: MR3147870
Digital Object Identifier: 10.1155/2013/697261

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI08 • 2013
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