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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 950482, 12 pages
A Fictitious Play Algorithm for Matrix Games with Fuzzy Payoffs
Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskişehir, Turkey
Received 2 February 2012; Accepted 6 August 2012
Academic Editor: Allan Peterson
Copyright © 2012 Emrah Akyar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, USA, 1944.
- K. H. Lee, First Course on Fuzzy Theory and Applications, vol. 27 of Advances in Intelligent and Soft Computing, Springer, Berlin, Germany, 2005.
- C. R. Bector and S. Chandra, Fuzzy Mathematical Programming and Fuzzy Matrix Games, vol. 169 of Studies in Fuzziness and Soft Computing, Springer, Berlin, Germany, 2005.
- J. Ramík and J. Římánek, “Inequality relation between fuzzy numbers and its use in fuzzy optimization,” Fuzzy Sets and Systems, vol. 16, no. 2, pp. 123–138, 1985.
- N. Furukawa, “A parametric total order on fuzzy numbers and a fuzzy shortest route problem,” Optimization, vol. 30, no. 4, pp. 367–377, 1994.
- N. Furukawa, “Parametric orders on fuzzy numbers and their roles in fuzzy optimization problems,” Optimization, vol. 40, no. 2, pp. 171–192, 1997.
- T. Maeda, “On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs,” Fuzzy Sets and Systems, vol. 139, no. 2, pp. 283–296, 2003.
- W. Amaral and F. Gomide, “An algorithm to solve two-person non-zero sum fuzzy games,” in Theoretical Advances and Applications of Fuzzy Logic and Soft Computing, O. Castillo, P. Melin, O. Ross, R. S. Cruz, W. Pedrycz, and J. Kacprzyk, Eds., vol. 42 of Advances in Soft Computing, pp. 296–302, Springer, Berlin, Germany, 2007.
- L. Campos, “Fuzzy linear programming models to solve fuzzy matrix games,” Fuzzy Sets and Systems, vol. 32, no. 3, pp. 275–289, 1989.
- E. Akyar and H. Akyar, “A graphical method for solving interval matrix games,” Abstract and Applied Analysis, vol. 2011, 17 pages, 2011.
- A. C. Cevikel and M. Ahlatçıoğlu, “Solutions for fuzzy matrix games,” Computers and Mathematics with Applications, vol. 60, no. 3, pp. 399–410, 2010.
- G. W. Brown, “Some notes on computation of games solutions,” RAND Report P-78, The RAND Corporation, Santa Monica, Calif, USA, 1949.
- J. Robinson, “An iterative method of solving a game,” Annals of Mathematics. Second Series, vol. 54, pp. 296–301, 1951.
- E. Akyar, H. Akyar, and S. A. Düzce, “Brown-Robinson method for interval matrix games,” Soft Computing, vol. 15, no. 10, pp. 2057–2064, 2011.
- W. D. Collins and C. Hu, “Studying interval valued matrix games with fuzzy logic,” Soft Computing, vol. 12, no. 2, pp. 147–155, 2008.