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 doi:

DOI: 10.3724/SP.J.1249.2018.01105

Journal of Shenzhen University Science and Engineering (深圳大学学报理工版) 2018/35:1 PP.105-109

## Information set generalized multi-objective games based on bounded rationality

• HE Jihao 1,2   XIANG Shuwen 2   JIA Wensheng 2   DENG Xicai 3
• 1.College of Computer Science and Technology, Guizhou University, Guiyang 550025, Guizhou Province, P. R. China;
• 2.School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou Province, P. R. China;
• 3.Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, Guizhou Province, P. R. China

Abstract：
On the base of the bounded rationality, we investigate the stability of the problem of the weak Pareto-Nash equilibrium for information set generalized multi-objective games. Based on the conclusion that the metric space of the problem of information set generalized multi-objective games are complete, the bounded rationality model is established according to the bounded rationality model described by the game theory language, and the result shows that the problem of the weak Pareto-Nash equilibrium is structurally stable and robust to ε-equilibrium by identifying some assumptions.

Key words：operation research,game theory,information sets generalized multio-bjective game,weak Pareto-Nash equilibrium point,bounded rationality,stability

ReleaseDate：2018-03-20 15:26:56

[1] BLACKWELL O. An analogy of minimax theorem for vector payoffs[J]. Pacific Journal of Mathematics, 1956, 6(1):1-8.

[2] SHAPLEY L S. Equilibrium points in games with vector payoffs[J]. Naval Research Logistics Quarterly, 1959, 6(1):57-61.

[3] 杨辉,俞建.向量拟平衡问题的本质解及解集的本质连通区[J].系统科学与数学,2004,24(1):74-84. YANG Hui, YU Jian. Essential solutions and essential components of solution set of vector quasi-equilibrium problems[J]. Journal of Systems Science and Mathematical Sciences, 2004, 24(1):74-84.(in Chinese)

[4] XIE Pingding. Nonempty intersection theorems and generalized multi-objective games in product FC-Spaces[J]. Journal of Global Optimization. 2007, 37(1):63-73.

[5] 贾文生,向淑文.信息集广义多目标博弈弱Pareto-Nash平衡点存在性和稳定性[J].运筹学学报,2015, 19(1):9-17. JIA Wensheng, XIANG Shuwen.Existence and stability of weakly Pareto-Nash equilibrium points for information sets generalized multi-objective games[J].Operations Research Transactions, 2015, 19(1):9-17.(in Chinese)

[6] ANDERLINI L, CANNING D. Structural stability implies robustness to bounded rationality[J]. Journal of Economic Theory, 2001, 101(2):395-422.

[7] YU Chao,YU Jian. On structural stability and robustness to bounded rationality[J]. Nonlinear Analysis:Theory, Methods & Applications, 2006, 65(3):583-592.

[8] YU Chao,YU Jian. Bounded rationality in multi-objective games[J]. Nonlinear Analysis:Theory, Methods & Applications, 2007, 67(3):930-937.

[9] 俞建.几类考虑有限理性平衡问题解的稳定性[J].系统科学与数学,2009,29(7):999-1008. YU Jian. Bounded rationality and stability of solutions of some equilibrium problems[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(7):999-1008.(in Chinese)

[10] YU Jian, YANG Hui, YU Chao. Structural stability and robustness to bounded rationality for non-compact cases[J]. Journal of Global Optimization, 2009, 44(1):149-157.

[11] 俞建.博弈论与非线性分析续论[M].北京:科学出版社,2011. YU Jian. Game theory and introduction of nonlinear analysis[M]. Beijing:Science Press, 2011.