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On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies

Author

Listed:
  • Svajone Bekesiene

    (Logistics and Defense Technology Management Science Group, General Jonas Zemaitis Military Academy of Lithuania, Silo 5a, LT-10322 Vilnius, Lithuania)

  • Serhii Mashchenko

    (Department of System Analysis and Decision-Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine)

Abstract

The present paper investigates a finite game with fuzzy sets of player strategies. It is proven that Nash equilibria constitute a type-2 fuzzy set defined on the universal set of strategy profiles. Furthermore, the corresponding type-2 membership function is provided. This paper demonstrates that the Nash equilibria type-2 fuzzy set of the game can be decomposed based on the secondary membership grades into a finite collection of crisp sets. Each of these crisp sets represents the Nash equilibria set of the corresponding game with crisp sets of player strategies. A characteristic feature of the proposed decomposition approach is its independence from the chosen method for calculating the Nash equilibria in crisp subgames. Some properties of game equilibria T2FSs are studied. These sets correspond to specific partitions or cuts of the original fuzzy sets of player strategies. An illustrative example is also included for clarity.

Suggested Citation

  • Svajone Bekesiene & Serhii Mashchenko, 2023. "On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies," Mathematics, MDPI, vol. 11(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4619-:d:1278251
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    References listed on IDEAS

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    3. Michael Aristidou & Sudipta Sarangi, 2006. "Games in Fuzzy Environments," Southern Economic Journal, John Wiley & Sons, vol. 72(3), pages 645-659, January.
    4. D. Garagic & J.B. Cruz, 2003. "An Approach to Fuzzy Noncooperative Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 475-491, September.
    5. Michael Aristidou & Sudipta Sarangi, 2006. "Games in Fuzzy Environments," Southern Economic Journal, John Wiley & Sons, vol. 72(3), pages 645-659, January.
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