策略型利他博弈中利他均衡研究

doi:10.15960/j.cnki.issn.1007-6093.2026.02.008

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 109-124.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.008

策略型利他博弈中利他均衡研究

王能发^1,2,†, 杨哲³

1. 贵州财经大学数学与统计学院, 贵州贵阳 550025;
2. 贵州财经大学大数据统计学院, 贵州贵阳 550025;
3. 上海财经大学经济学院, 上海 200433

收稿日期:2023-01-13 发布日期:2026-06-12
通讯作者: 王能发 E-mail:nengfa_wang@163.com
基金资助:
贵州省基础研究计划 (自然科学) 项目 (No. 黔科合基础 MS[2025]231),贵州财经大学创新探索及学术新苗项目 (No. 2024XSXMB22)

Research on altruistic equilibria in altruistic strategy-form games

WANG Nengfa^1,2,†, YANG Zhe³

1 School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China;
2 College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China;
3 School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China

Received:2023-01-13 Published:2026-06-12

摘要/Abstract

摘要： 本文在策略型利他博弈中假定参与人是利他的,基于此假设,引入具有偏好映射的利他博弈与利他广义博弈,并证明博弈模型中利他均衡的存在性定理。作为应用,我们在规范型博弈和不同广义博弈中给出利他均衡存在性结论。

关键词: 利他博弈, 利他均衡, 偏好映射, 外部性偏好

Abstract: In this paper, we assume that the players are altruistic in strategy-form games. Following the idea, we introduce the altruistic games and altruistic generalized games with preference correspondences, and prove the existence theorems of altruistic equilibria. As applications, we obtain the existence theorems of altruistic equilibria for normal-form games and generalized games.

Key words: altruistic game, altruistic equilibria, preference correspondence, external preference

中图分类号:

O225

王能发, 杨哲. 策略型利他博弈中利他均衡研究[J]. 运筹学学报（中英文）, 2026, 30(2): 109-124.

WANG Nengfa, YANG Zhe. Research on altruistic equilibria in altruistic strategy-form games[J]. Operations Research Transactions, 2026, 30(2): 109-124.

参考文献

[1] Nash J. Non-cooperative games [J]. Annals of Mathematics, 1951, 54(2): 286-295.
[2] Glicksberg I L. A further generalization of the Kakutani fixed point theorem with applications to Nash equilibrium points [J]. Proceedings American Mathematical Society, 1952, 3(1): 170- 174.
[3] Yu J. Essential equilibria of n-person noncooperative games [J]. Journal of Mathematical Economics, 1999, 31(3): 361-372.
[4] Shafer W, Sonnenschein H. Equilibrium in abstract economies without ordered preferences [J]. Journal of Mathematical Economics, 1975, 2(3): 345-348.
[5] Yang Z, Song Q. A unified approach to the Nash equilibrium existence in large games from finitely many players to infinitely many players [J]. Journal of Fixed Point Theory and Applications, 2022, 24: 11.
[6] Bolton G E, Ockenfels A. ERC: A theory of equity, reciprocity, and competition [J]. American Economic Review, 2000, 90(1): 166-193.
[7] Colman A M, Korner T W, Musy O, et al. Mutual support in games: some properties of Berge equilibria [J]. Journal of Mathematical Psychology, 2011, 55(2): 166-175.
[8] Rabin M. Incorporating fairness into game theory and economics [J]. American Economic Review, 1993, 83(5): 1281-1302.
[9] Rabin M. Review of the rational foundations of economic behaviour: Proceedings of the IEA conference held in Turin, Italy [M]//Arrow K J, Colombatto E, Perlman M, et al. (eds.) The Rational Foundation of Economic Behaviour, London: Macmillan Press, 1996: 2045-2046.
[10] Rabin M. A perspective on psychology and economics [J]. European Economic Review, 2002, 46(4-5): 657-685.
[11] Dufwenberg M, Kirchsteiger G. A theory of sequential reciprocity [J]. Games and Economic Behavior, 2004, 47: 268-298.
[12] 蒲勇健. 建立在行为经济学理论基础上的委托代理模型: 物质效用与动机公平的替代 [J]. 经济学(季刊), 2008(1): 297-318.
[13] Fehr E, Schmidt K M. A theory of fairness, competition, and cooperation [J]. The Quarterly Journal of Economics, 1999, 114(3): 817-868.
[14] Nowak M A, Sigmund K. Evolution of indirect reciprocity [J]. Nature, 2005, 437: 1291-1298.
[15] Marco G, Morgan J. Slightly altruistic equilibria [J]. Journal of Optimization Theory & Applications, 2008, 137(2): 347-362.
[16] 俞建．$n$ 人非合作博弈的轻微利他平衡点[J]系统科学与数学, 2011, 31: 534-539.
[17] 蒲勇健, 杨哲. 轻微利他弱~Pareto-Nash 均衡 [J]. 系统科学与数学, 2010, 30(9): 1259-1266.
[18] 王能发. 基于轻微利他均衡的古诺博弈研究 [J]. 重庆师范大学学报(自然科学版), 2014, 31(4): 26-29.
[19] Karagozoglu E, Keskin K, Saglam C. A minimally altruistic refinement of Nash equilibrium [J]. Mathematical Social Sciences, 2013, 66: 422-430.
[20] Garcia-Martinez J A, Vega-Redondo F. Social cohesion and the evolution of altruism [J]. Games and Economic Behavior, 2015, 92: 74-105.
[21] Scalzo V. Other-regarding behaviour in fuzzy non-cooperative games: Existence of altruistic equilibria [J]. Fuzzy Sets and Systems, 2023, 458: 118-125.
[22] Deguire P, Tan K K, Yuan X Z. The study of maximal elements, fixed points for LS-majorized mappings and their applications to minimax and variational inequalities in product topological spaces [J]. Nonlinear Analysis Theory Methods & Applications, 1999, 37(7): 933-951.
[23] Tarafdar E U, Chowdhury M S R. Topological Methods for Set-Valued Nonlinear Analysis [M]. Singapore: World Scientific Publishing Co Pte Ltd, 2008.

策略型利他博弈中利他均衡研究

Research on altruistic equilibria in altruistic strategy-form games

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