Constrained Bimatrix Games with Fuzzy Goals and its Application in Nuclear Negotiations

Document Type : Research Article

Authors

• H. Bigdeli ¹
• H. Hassanpour ²
• J. Tayyebi ³

¹ Researcher, Institute for the Study of War, Command and Staff University, Tehran, I.R. Iran army.

² University of Birjand, Birjand,

³ Birjand University of Technology, Birjand,

10.22067/ijnao.v8i1.55385

Abstract

Solving constrained bimatrix games in the fuzzy environment is the aim of this research. This class of two-person nonzero-sum games is considered with finite strategies and fuzzy goals when some additional linear constraints are imposed on the strategies. We consider constrained two-person nonzero sum games with single and multiple payoffs. It is shown that an equilibrium solution of single-objective case can be characterized by solving a quadratic programming problem with linear constraints. Some mathematical program ming problems are also introduced to obtain the equilibrium points in multi objective case with crisp and fuzzy constraints. Finally, a political application of such games is presented which is about nuclear negotiations between two countries.

Keywords

• Multiobjective game
• Constrained game
• Fuzzy constrained game
• Nuclear negotiations

20.1001.1.24236977.2018.8.1.5.1

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