多选择NTU结构对策下的社会稳定核心

doi:10.12005/orms.2017.0032

运筹与管理 ›› 2017, Vol. 26 ›› Issue (2): 49-56.DOI: 10.12005/orms.2017.0032

多选择NTU结构对策下的社会稳定核心

田海燕¹, 王志巍², 郑小伟², 张刚²

1.西北工业大学理学院应用数学系,陕西西安 710072;
2.河北师范大学数学与信息科学学院,河北石家庄 050024

收稿日期:2015-11-21 出版日期:2017-02-25
作者简介:田海燕(1972-),女,博士生,副教授,研究方向为对策论及其应用、算法设计;王志巍(1960- ),男,硕士,副教授,研究方向为图论、算法、图像处理;郑小伟(1979-),男,博士,研究方向为图论及其应用;张刚(1970-),男,博士,教授,研究方向为动力学与控制论。
基金资助:
河北省自然科学基金资助项目(A2014205152)

Social Stable Cores for Multi-choice NTU Structured Games

TIAN Hai-yan¹, WANG Zhi-wei², ZHENG Xiao-wei², ZHANG Gang²

1.Department of Applied Mathematics, School of Science Northwestern Polytechnical University, Xi’an 710072, China;
2.College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

Received:2015-11-21 Online:2017-02-25

摘要/Abstract

摘要： 本文研究了多选择情形下NTU结构对策及其社会稳定核心的理论和应用。定义了多选择NTU结构对策的转移率规则和支付依赖平衡性质,给出了K-K-M-S定理在多选择NTU结构对策下的一个扩展形式,并用扩展后的K-K-M-S定理证明了如果转移率规则包含某些力量函数值,且多选择NTU结构对策关于转移率规则是支付依赖平衡的,则多选择NTU结构对策的社会稳定核心是非空的。

关键词: 多选择NTU对策, 结构对策, 核心, K-K-M-S定理, 支付依赖平衡

Abstract: This paper deals with the theory and applications of multi-choice NTU structured games and socially stable cores. Transfer rate rule and payoff-dependent balancedness for multi-choice NTU structured games are introduced and an extension of K-K-M-S theorem is provided in multi-choice NTU structured games. By using the extension of K-K-M-S theorem, we prove that if transfer rate rule includes some values of power functions, and a multi-choice NTU structured game is payoff-dependent balanced with respect of the rule,then the game has a non-empty socially stable core.

Key words: multi-choice NTU games, structured games, cores, K-K-M-S theorem, payoff-dependent balancedness

中图分类号:

O225

田海燕, 王志巍, 郑小伟, 张刚. 多选择NTU结构对策下的社会稳定核心[J]. 运筹与管理, 2017, 26(2): 49-56.

TIAN Hai-yan, WANG Zhi-wei, ZHENG Xiao-wei, ZHANG Gang. Social Stable Cores for Multi-choice NTU Structured Games[J]. Operations Research and Management Science, 2017, 26(2): 49-56.

参考文献

[1] Inoue T. Representation of non-transferable utility games by coalition production economies[J]. Journal of Mathematical Economics, 2013, 49: 141-149.
[2] Liu J, Liu X. Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies[J]. International Journal of Game Theory, 2014, 43: 975-990.
[3] Scarf H. The core of an n-person game[J]. Econometrica, 1967, 35: 50-69.
[4] Shapley L S. On balanced games without side payments. In: Hu T C, Robinson S M(Eds.). Mathematical Programming[M]. Academic Press, New York, 1973: 261-290.
[5] Liu J, Tian H. Existence of fuzzy cores and generalizations of the K-K-M-S theorem[J]. Journal of Mathematical Economics, 2014, 52: 148-152.
[6] Bonnisseau J M, Iehl V. Payoff-dependent balancedness and cores[J]. Games and Economic Behavior, 2007, 61: 1-26.
[7] Billera L J. Some theorems on the core of an n-person game without side-payments[J]. SIAM Journal of Applied Mathematics, 1970, 18: 567-579.
[8] Keiding H. Thorlund-petersen. the core of a cooperative game without side-payments[J]. Journal of Optimization Theory and Applications, 1987, 54: 273-288.
[9] Predtetchinski A, Herings J J. A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game[J]. Journal of Economic Theory, 2004, 116: 84-92.
[10] Herings P J J, van der Laan G, Talman D. Socially structured games[J]. Theory and Decision, 2007, 62: 1-29.
[11] van den Brink R, Gilles R P. Measuring domination in directed graph[J]. Socially Networks, 2000, 22: 1141-1157.
[12] Rubinstein A. Ranking the participants in a tournament[J]. SIAM Journal of Applied Mathematics, 1980, 38: 108-111.
[13] Fan K. Extensions of two fixed point theorems of F. E. Browder[J]. Mathematische Zeitschrift, 1969, 112: 234-240.
[14] Kannai Y. The cores and balancedness. in: aumann R J, Hart S(Eds.). handbook of game theory with economic applications[M]. North-Holland, Amsterdam, 1992: 355-395.
[15] Hwang Y, Li W. The core of multi-choice NTU games[J]. Mathematical Methods of Operations Research, 2005, 61: 33-40.

多选择NTU结构对策下的社会稳定核心

Social Stable Cores for Multi-choice NTU Structured Games

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

编辑推荐

Metrics

[1]	周华蓉, 贺胜兵, 刘友金. 后发企业突破低端锁定的三方演化博弈分析[J]. 运筹与管理, 2021, 30(12): 58-64.
[2]	赵连霞, 张小峰, 岳超楠, 王芳晴, 尤建新. 供应商生产违规下政府与核心企业审查策略研究[J]. 运筹与管理, 2021, 30(11): 203-210.
[3]	李文立, 赵帅. 考虑溯源系统应用的优质农产品双渠道供应链决策研究[J]. 运筹与管理, 2019, 28(6): 98-108.
[4]	关菲, 栗军. 区间合作对策核心存在性的进一步讨论[J]. 运筹与管理, 2018, 27(4): 10-14.
[5]	周意元,张强. 具有区间支付的宗派对策[J]. 运筹与管理, 2016, 25(2): 57-62.
[6]	周意元, 张强. 排序对策的一个新的收益分配准则[J]. 运筹与管理, 2015, 24(6): 11-15.
[7]	孙红霞. 基于Choquet积分形式的模糊联盟核心[J]. 运筹与管理, 2015, 24(1): 93-99.
[8]	杨皎平, 张恒俊, 侯楠. 集群企业间关系强度对合作技术创新的影响——基于企业类型和创新类型的视角[J]. 运筹与管理, 2015, 24(1): 280-287.
[9]	李泉林, 段灿, 鄂成国, 杨碧蕊. 云资源提供商的合作博弈模型与收益分配研究[J]. 运筹与管理, 2014, 23(4): 274-275.
[10]	郭菊花, 高作峰. 直觉模糊支付合作对策的核仁解[J]. 运筹与管理, 2014, 23(3): 102-107.