集值群体博弈 Nash 均衡与合作均衡的广义适定性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1217-1228.

集值群体博弈 Nash 均衡与合作均衡的广义适定性

葛晨¹,陈卓正²,张宇^1,^*()

¹云南财经大学统计与数学学院昆明 650221
²中国石油大学 (华东) 理学院山东青岛 266580

收稿日期:2024-10-29 修回日期:2025-06-06 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: zhangyu198606@sina.com
基金资助:
国家自然科学基金(11901511);云南省基础研究基金(202501AT070447);云南省兴滇英才青年人才专项基金

Generalized Well-Posedness of Nash Equilibrium and Cooperative Equilibrium for Population Games with Set Payoffs

Ge Chen¹,Chen Zhuozheng²,Zhang Yu^1,^*()

¹Yunnan University of Finance and Economics, School of Statistics and Mathematics, Kunming 650221
²China University of Petroleum, College of Science, Shandong Qingdao 266580

Received:2024-10-29 Revised:2025-06-06 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(11901511);Yunnan Fundamental Research Projects(202501AT070447);Xingdian Talents Project Foundation for Young Scholar in Yunnan Province

摘要/Abstract

摘要：

借助一类非线性标量函数, 分别构建集值群体博弈 Nash 均衡与合作均衡的有限理性函数, 研究有限理性函数的下半连续性质, 并建立其零水平集与博弈均衡集之间的等价关系. 利用有限理性函数的所得性质, 得到集值群体博弈 Nash 均衡与合作均衡的广义适定性.

关键词: Nash 均衡, 合作均衡, 集支付, 群体博弈, 广义适定性

Abstract:

By using a class of nonlinear scalarization functions, we construct the bounded rationality functions of Nash equilibrium and cooperation equilibrium of population games with set payoffs, respectively. Then, we show the lower semicontinuity of the bounded rationality functions and the equivalence relations between their level sets of zero and game equilibrium sets. Finally, employing the acquired properties of the bounded rationality functions, we prove the generalized well-posedness of Nash equilibrium and cooperative equilibrium for set payoffs population games.

Key words: Nash equilibrium, cooperative equilibrium, set payoff, population games, generalized well-posedness

中图分类号:

O225

葛晨, 陈卓正, 张宇. 集值群体博弈 Nash 均衡与合作均衡的广义适定性[J]. 数学物理学报, 2025, 45(4): 1217-1228.

Ge Chen, Chen Zhuozheng, Zhang Yu. Generalized Well-Posedness of Nash Equilibrium and Cooperative Equilibrium for Population Games with Set Payoffs[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1217-1228.

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