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Main diagonal dominant principle and algorithm of equilibrium in joint mixed strategies for bimatrix games
DAI Ye-ming, GAO Hong-wei, XU Mi, WANG Gui-rong, XUAN Hai, YIN Lian-ling
Systems Engineering - Theory & Practice ›› 2013, Vol. 33 ›› Issue (6) : 1523-1529.
PDF(529 KB)
PDF(529 KB)
Main diagonal dominant principle and algorithm of equilibrium in joint mixed strategies for bimatrix games
The main diagonal dominant principle is put forward to judge equilibrium in joint mixed strategies for bimatrix games. We discuss the relationship between mixed strategies and joint mixed strategies, and the relationship between Nash equilibrium and equilibrium in joint mixed strategies, in terms of payment. And we find equilibrium in joint mixed strategies through improved PSO algorithm.
bimatrix game / equilibrium in joint mixed strategies / main diagonal dominant principle / PSO algorithm {{custom_keyword}} /
[1] Aumann R J. Subjectivity and correlation in randomized strategies[J]. Journal of Mathematical Economics, 1974, 1: 67-96.
[2] Aumann R J. Correlated equilibrium as an expression of Bayesian rationality[J]. Econometrica, 1987, 55: 1-18.
[3] Petrosjan L A, Zenkevich N A. Game theory[M]. World Scientific Publisher, 1996.
[4] 余谦, 王先甲. 基于粒子群优化求解纳什均衡的演化算法[J]. 武汉大学学报:理学版, 2006, 52(1): 25-29.Yu Q, Wang X J. Evolutionary algorithm for solving Nash equilibrium based on particle swarm optimization[J]. Journal of Wuhan University: Natural Science Edition, 2006, 52(1): 25-29.
[5] 刘伟兵, 王先甲. 基于PSO神经网络的进化博弈研究[J]. 系统工程与电子技术, 2007, 29(8): 1282-1284.Liu W B, Wang X J. Study on evolutionary games based on PSO-neural networks[J]. Systems Engineering and Electronics, 2007, 29(8): 1282-1284.
[6] Pavlidis N G, Parsopoulos K E, Vrahatis M N. Computing Nash equilibria through computational intelligence methods[J]. Journal of Computational and Applied Mathematics, 2005, 175: 113-136.
[7] Bosse H, Byrka J, Markakis E. New algorithms for approximate Nash equilibria in bimatrix games[J]. Theoretical Computer Science, 2010, 411: 164-173.
[8] Jiang Y, Hu T S, Huang C C, et al. An improved particle swarm optimization algorithm[J]. Applied Mathematics and Computation, 2007, 193: 231-239.
[9] Pedersen M E H, Chipperfield A J. Simplifying particle swarm optimization[J]. Applied Soft Computing, 2010, 10: 618-628.
[10] 高红伟, (俄)彼得罗相. 动态合作博弈[M]. 北京: 科学出版社, 2009.Gao H W, Petrosyan L A. Dynamics cooperative games[M]. Beijing: Science Press, 2009.
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