SOLUTION CONCEPT FOR A NON-COOPERATIVE GAME WITH FUZZY PARAMETERS

Fatiha Kacher () and Moussa Larbani ()
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Fatiha Kacher: Department of Mathematics, Faculty of Sciences, University of Tizi-Ouzou, Tizi-Ouzou, 15000, Algeria
Moussa Larbani: Department of Mathematics, Faculty of Sciences, University of Tizi-Ouzou, Tizi-Ouzou, 15000, Algeria

International Game Theory Review (IGTR), 2006, vol. 08, issue 03, 489-498

Abstract: In this paper, we study a non cooperative game with payoff functions involving fuzzy parameters. We introduce a concept of solution for this game that we call α-N-S- equilibrium. Our definition is derived from the concept of N-S equilibrium introduced by Zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior. The α-N-S- equilibrium takes into account both the aspect of conflict and the aspect of decision making under uncertainty related to the presence of fuzzy parameters. For the aspect of conflict we adopted the Nash equilibrium, for the aspect of uncertainty we adopted the maximin approach through weak Pareto optimality. Furthermore, we give sufficient conditions for its existence.

Keywords: Fuzzy set; non-cooperative game; Nash equilibrium; weak Pareto optimality (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219198906001041

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