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Solution Concept For A Non-Cooperative Game With Fuzzy Parameters

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fatiha Kacher & Moussa Larbani, 2006. "Solution Concept For A Non-Cooperative Game With Fuzzy Parameters," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 489-498.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:03:n:s0219198906001041
    DOI: 10.1142/S0219198906001041
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    More about this item

    Keywords

    Fuzzy set; non-cooperative game; Nash equilibrium; weak Pareto optimality;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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