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Monte Carlo Methods In Fuzzy Game Theory

Author

Listed:
  • AREEG ABDALLA

    (Mathematics Department, University of Alabama at Birmingham, Birmingham, Alabama, 35294, USA)

  • JAMES BUCKLEY

    (Mathematics Department, University of Alabama at Birmingham, Birmingham, Alabama, 35294, USA)

Abstract

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players($\overline{V}_I$,$\overline{V}_{II}$)and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values$\overline{V}_I$for Player I and$\overline{V}_{II}$for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at$\overline{V}_I$and$\overline{V}_{II}$to see if there is a Minimax theorem($\overline{V}_I = \overline{V}_{II}$)for this fuzzy game.

Suggested Citation

  • Areeg Abdalla & James Buckley, 2007. "Monte Carlo Methods In Fuzzy Game Theory," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 259-269.
    • Handle: RePEc:wsi:nmncxx:v:03:y:2007:i:02:n:s1793005707000768
    DOI: 10.1142/S1793005707000768
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    Cited by:

    1. Kose, Erkan & Erbas, Mehmet & Ersen, Erkan, 2017. "An integrated approach based on game theory and geographical information systems to solve decision problems," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 105-114.

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