# Monte Carlo Methods In Fuzzy Game Theory

## Author Info

• 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)

Registered author(s):

## 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.

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## Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

Volume (Year): 03 (2007)
Issue (Month): 02 ()
Pages: 259-269

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 Handle: RePEc:wsi:nmncxx:v:03:y:2007:i:02:p:259-269 Contact details of provider: Web page: http://www.worldscinet.com/nmnc/nmnc.shtml Order Information: Email:

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