超图结构上合作博弈的赋权Position值

doi:10.12005/orms.2022.0281

运筹与管理 ›› 2022, Vol. 31 ›› Issue (9): 28-33.DOI: 10.12005/orms.2022.0281

超图结构上合作博弈的赋权Position值

单而芳¹, 谢娜娜¹, 王光明^1,2

1.上海大学管理学院,上海 200444;
2.济南大学数学科学学院,山东济南 250022

收稿日期:2017-08-10 出版日期:2022-09-25 发布日期:2022-10-21
通讯作者: 王光明(1980-),男,山东济南,副教授,博士研究生,研究方向:图上合作博弈。
作者简介:单而芳(1965-),男,河北石家庄,教授,博士生导师,研究方向:图论及其应用, 图上合作博弈。
基金资助:
国家自然科学基金资助项目(11971298)

The Weighted Position Value for HypergraphGames

SHAN Er-fang¹, XIE Na-na¹, WANG Guang-ming^1,2

1. School of Management, Shanghai University, Shanghai 200444, China;
2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received:2017-08-10 Online:2022-09-25 Published:2022-10-21

摘要/Abstract

摘要： 在合作博弈的一般模型中总是假设所有联盟都能形成。不过,在实际中由于受到一些因素的制约,有些联盟是不能形成的。基于此,Myerson提出了具有图通讯结构的合作博弈。Myerson值和Position值是超图博弈上的两个重要分配规则。2005年,Slikker给出了在图博弈上Position值的公理化刻画。但超图博弈上Position值的公理化刻画一直悬而未决。本文通过引入 “赋权平衡超边贡献公理”,并结合经典的“分支有效性”,提出了超图博弈上赋权Position值的公理化刻画。作为推论,解决了超图博弈上Position值的公理化刻画问题。

关键词: 超图, TU-博弈, 超图博弈, Myerson值, 赋权Position值

Abstract: In the general model of cooperative game, it is always assumed that all coalitions can be formed. However, in practice, due to the constraints of some factors, some coalitions can not be formed. Based on this, Myerson proposed a cooperative game with graph communication structures. The Myerson value and position value are two important allocation rules in hypergraph games. In 2005, Slikker gave an axiomatic characterization of position values on graph games. However, the axiomatic characterization of position values in hypergraph games is still up in the air. In this paper, by introducing the axiom of weighted balanced conference contributions, and combining with the classical component efficiency, the axiomatic characterization of weighted positioning values on hypergraph games is proposed. As a corollary, the problem of axiomatic characterization of position values on hypergraph games is solved.

Key words: hypergraph, TU-game, hypergraph games, myerson value, position valuewith weight structure

中图分类号:

单而芳, 谢娜娜, 王光明. 超图结构上合作博弈的赋权Position值[J]. 运筹与管理, 2022, 31(9): 28-33.

SHAN Er-fang, XIE Na-na, WANG Guang-ming. The Weighted Position Value for HypergraphGames[J]. Operations Research and Management Science, 2022, 31(9): 28-33.

参考文献

[1] Branzei R, Dimitrov D, Tijs S. Models in cooperative game 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 AW,Kuhn HW(eds.). Contributions to the Theory of Games II. Princeton: Princeton University Press, 1953: 307-317.
[4] Li D L, Shan E. Safety of links with respect to the myerson valuefor communication situations[J]. Operational Research, https://doi.org/10.1007/s12351-020-00602-5.
[5] 单而芳,刘珍.边赋权图对策Myerson值的和分解[J].运筹与管理,2020,29(10):102-125.
[6] Li D L, Shan E. The Myerson value for directed graph games[J]. Operations Research Letters, 2020, 48: 42-46.
[7] Shan E, Han J, Shi. The efficient proportional myerson values[J]. Operations Research Letters, 2019, 47: 574-578.
[8] Li D L, Shan E. The myerson valueon local structures of coalitions[J]. Journal of the Operations Research Society of China, 2019, 7: 461-473.
[9] Meessen R. Communication games, master's thesis, department of mathematics[D]. University of Nijmegen, the Netherlands(in Dutch), 1988.
[10] Borm P, Owen G, Tijs S. On the position value for communication situations[J]. SIAM Journal on Discrete Mathematics, 1992, 5(3): 305-320.
[11] 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.
[12] Algaba E, Bilbao J M, Borm P, Lopez J J. The position value for union stable systems[J]. Mathematical Methods of Operation Research, 2000, 52(2): 221-236.
[13] Slikker M. A characterization of the position value[J]. International Journal of Game Theory, 2005, 33(4): 505-514.
[14] 单而芳,吕文蓉,史纪磊.具有联盟结构的Position值[J].运筹与管理,2021,30(3):112-116.
[15] 李思文,赵家贵,单而芳.超网络博弈的Position值的公理化刻画[J].运筹学学报,2019,23(4):165-174.
[16] 单而芳,李康,刘珍.具有超图合作结构的赋权Position值[J].运筹与管理,2019,28(6):109-117.
[17] Li D L, Shan E. The position value and the structures of graphs[J]. Applied Mathematics and Computation, 2019, 356: 190-197.
[18] Shapley L S. Additive and non-additive set functions. PhD Thesis, Department of Mathematics, Princeton University, 1953.
[19] Haeringer G. Weighted myerson value[J]. International Game Theory Review, 1999, 1(2): 187-192.
[20] Slikker M, van den Nouweland A. Communication situations with asymmetric players[J]. Mathematical Methods of Operations Research, 2000, 52(1): 39-56.
[21] Gonzalez-Aranguena E, Manuel C M, Pozo M. Values of games with weighted graphs[J]. European Journal of Operational Research, 2015, 243(3): 248-257.
[22] Ghintran A, Gonzalez-Aranguena E, Manuel C. A probabilistic positionvalue[J]. Annals of Operation Research, 2012, 2(1): 183-196.
[23] Ghintran A. Weighted position values[J]. Mathematical Social Sciences, 2013, 65(2): 157-163.
[24] Harsanyi J C. A bargaining model for the cooperative n-person game[J]. Contributions to the Theory of Games, 1959, 40(4): 325-355.
[25] Shan E, Zhang G, Dong Y. Component-wise proportionalsolutions for communication graph games[J]. Mathematical Social Sciences, 2016, 81(1): 22-28.

超图结构上合作博弈的赋权Position值

The Weighted Position Value for HypergraphGames

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