MONTE CARLO METHODS IN FUZZY GAME THEORY

Areeg Abdalla () and James Buckley ()
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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

New Mathematics and Natural Computation (NMNC), 2007, vol. 03, issue 02, 259-269

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.

Keywords: Fuzzy game theory; Monte Carlo; random fuzzy vectors (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S1793005707000768

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