超网络博弈的位置值的公理化刻画

doi:10.15960/j.cnki.issn.1007-6093.2019.04.015

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 165-174.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.015

• • 上一篇

超网络博弈的位置值的公理化刻画

李思文¹, 赵加贵², 单而芳^1,*

1. 上海大学管理学院, 上海 200444;
2. 上海公安学院, 上海 200137

收稿日期:2017-12-18 发布日期:2019-12-04
通讯作者: 单而芳 E-mail:efshan@shu.edu.cn
基金资助:
国家自然科学基金（No.11971298）

A characterization of the position value for hypernetwork situations

LI Siwen¹, ZHAO Jiagui², SHAN Erfang^1,*

1. School of Management, Shanghai University, Shanghai 200444, China;
2. Shanghai Police College, Shanghai 200137, China

Received:2017-12-18 Published:2019-12-04

摘要/Abstract

摘要： 在图博弈中，Myerson假设只有连通的联盟才能获得完全的效用，而忽略连通联盟的具体结构.1996年，Jackson和Wolinsky提出了“网络情形博弈”的模型，拓展了Myerson的图博弈模型.它是利用值函数代替原来的特征函数以体现不同网络结构对合作结果的影响.考虑超网络情形博弈，它是网络情形博弈的自然推广，由三元组（N，H，v）所组成，这里v是值函数，用于描述在超网络（N，H）合作结构下的合作收益.2012年，van den Nouweland和Slikker利用四个公理给出了位置值的公理化刻画.通过分支有效性和局部平衡超边贡献性两个公理，给出了超网络博弈中位置值的公理化刻画.作为推论，得到了网络博弈中位置值的新刻画.

关键词: 超网络博弈, 位置值, 分支有效, 局部平衡超边贡献

Abstract: In graph games, Myerson assumed that only connected coalitions achieve fully the worth, but the structures of coalitions are ignored. In 1996, Jackson and Wolinsky generalized the Myerson’s model to “network situation”. The characteristic function is replaced by the value function to reflect the influence of the structures on benefits of feasible coalitions. In this paper we consider hypernetwork situations, which is a natural extension on network situations. It consists of a triple (N, H, v) where (N, H) is a hypernetwork and v is the value function to describe the possible gains from TU-games, whose cooperation is restricted by a hypernetwork. In 2012, van den Nouweland and Slikker characterized the position value axiomatically for network situations by using four axioms. By introducing a new axiom, called partial balanced conference contributions, and combining component efficiency, we propose an axiomatic characterization of the position value for hypernetwork situations. As an immediate corollary, we give a new characterization of the position value for network situations.

Key words: hypernetwork situation, position value, component efficiency, partial balanced conference contributions

中图分类号:

李思文, 赵加贵, 单而芳. 超网络博弈的位置值的公理化刻画[J]. 运筹学学报, 2019, 23(4): 165-174.

LI Siwen, ZHAO Jiagui, SHAN Erfang. A characterization of the position value for hypernetwork situations[J]. Operations Research Transactions, 2019, 23(4): 165-174.

参考文献

[1] Branzei R, Dimitrov D, Tijs S. Models in Cooperative Bame Theory[M]. Berlin:Springer, 2008.
[2] Myerson R B. Graphs and cooperation in games[J]. Mathematics of Operations Research, 1977, 2(3):225-229.
[3] Shapley L S. A value for n-person games[A]. In:Tucker A W, Kuhn H W (eds.). Contributions to the Theory of Games II[C]. Princeton:Princeton University Press, 1953:307-317.
[4] Myerson R B. Conference structures and fair allocation rules[J]. International Jouanal of Game Theory, 1980, 9(3):169-182.
[5] Slikker M, van den Nouweland A. Social and Economic Networks in Cooperative Game Theory[M]. New York:Springer, 2001.
[6] Meessen R. Communication games[D]. Netherlands:University of Nijmegen (in Dutch), 1988.
[7] Borm P, Owen G, Tijs S. On the position value for communication situations[J]. SIAM Journal on Discrete Mathematics, 1992, 5(3):305-320.
[8] van den Nouweland A, Borm P, Tijs S. Allocation rules for hypergraph communication situations[J]. International Journal of Game Theory, 1992, 20(3):255-268.
[9] Algaba E, Bilbao J M, Borm P, et al. The Myerson value for union stable structres[J]. Mathematical Methods of Operation Research, 2001, 54(3):359-371.
[10] Slikker M. A characterization of the position value[J]. International Journal of Game Theory, 2005, 33(4):505-514.
[11] Li D L, Shan E. The position value and the structures of graphs[J]. Applied Mathematics and Computation, 2019, 356:190-197.
[12] Jackson M, Wolinsky A. A strategic model of social and economic networks[J]. Journal of Economic Theory, 1996, 71(1):44-74.
[13] Jackson M O. Allocation rules for network games[J]. Games and Economic Behavior, 2005, 51(1):128-154.
[14] Slikker M. Link monotonic allocation schemes[J]. International Game Theory Review, 2005, 7(4):419-429.
[15] van den Nouweland A, Slikker M. An axiomatic characterization of the position value for network situations[J]. Mathematical Social Sciences, 2012, 64(6):266-271.
[16] 李理, 单而芳. 图上合作博弈和图的边密度[J]. 运筹学学报, 2018, 22(4), 99-107.
[17] 单而芳, 李康, 刘珍. 具有超图合作结构的赋权位置值[J]. 运筹与管理, 2019, 28(6):109-117.
[18] Shan E, Zhang G. The Position value and the Myerson value for hypergraph communication situations, in:Petrosyan L A et al. (eds.), Frontiers of Dynamic Games, Static & Dynamic Game Theory:Foundations & Applications[M]. Springer, 2018, 237-250.

超网络博弈的位置值的公理化刻画

A characterization of the position value for hypernetwork situations

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