Profit Allocation Based on Graph Games

Operations Research and Management Science ›› 2013, Vol. 22 ›› Issue (4): 1-5.

• Theory Analysis and Methodology Study • Next Articles

Profit Allocation Based on Graph Games

NIE Cui-ping^1,2, ZHANG Qiang¹, ZHAO Xuan¹

1. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China;
2. Department of Mathematics and Information Science, Shijiazhuang College, Shijiazhuang 050035, China

Received:2012-03-03 Online:2013-08-25

基于图对策的收益分配

聂翠平^1,2, 张强¹, 赵璇¹

1.北京理工大学管理与经济学院,北京 100081;
2.石家庄学院数学与信息科学系,河北石家庄 050035

作者简介:聂翠平 (1980-),女,讲师,博士生,研究方向:模糊对策与决策;张强,男,教授,博士生导师,研究方向:对策与决策、模糊数学、供应链与物流管理等。
基金资助:
国家自然科学基金资助项目(70771010,71071018,70801064);高等学校博士学科点专项科研基金(20111101110036);石家庄市科学技术研究与发展计划课题(135790075A)

Abstract

Abstract: We study cooperative games with communication structure, called graph games. The generalization of the average tree solution is considered in the game. We propose that additivity axiom characterizes the solution. Furthermore, on the class of cycle-free graph games the solution satisfies component efficiency. The change in payoff can be represented by the average tree solution when a link between two players is deleted for a component that does not hold for Shapley value and the Myerson value. Finally, we show that there are similar properties in graph games with fuzzy coalitions.

Key words: graph game, average tree solution, fuzzy coalition, component efficiency, imputation

摘要： 基于具有交流结构的合作对策,即图对策,对平均树解拓展形式的特征进行刻画,提出此解满足可加性公理。进一步地,分析了对于无圈图对策此解是分支有效的。并且当连通分支中两个局中人相关联的边删掉后,此连通分支的收益变化情况可用平均树解表示。这一性质是Shapley值和Myerson值所不具有的。最后,我们给出了模糊联盟图对策中模糊平均树解的可加性和分支有效性。

关键词: 图对策, 平均树解, 模糊联盟, 分支有效性, 分配

CLC Number:

O225

NIE Cui-ping, ZHANG Qiang, ZHAO Xuan. Profit Allocation Based on Graph Games[J]. Operations Research and Management Science, 2013, 22(4): 1-5.

聂翠平, 张强, 赵璇. 基于图对策的收益分配[J]. 运筹与管理, 2013, 22(4): 1-5.

References

[1] Myerson R B. Graphs and cooperation in games[J]. Mathematics of Operations Research, 1977, 2: 225-229.
[2] Myerson R B. Conference structures and fair allocation rules[J]. International Journal of Game Theory, 1980, 9: 169-182.
[3] Borm P, Owen G, Tijs S. On the position value for communication situations[J]. SIAM Journal on Discrete Mathematics, 1992, 5: 305-320.
[4] Demange G. On group stability in hierarchies and networks[J]. Journal of Political Economy, 2004, 112: 754-778.
[5] Slikker M. A characterization of the position value[J]. International Journal of Game Theory, 2005, 33: 505-514.
[6] Talman D, Yamamoto Y. Average tree solution and subcore for acyclic graph games[J]. Journal of the Operations Research Society of Japan, 2008, 51(3): 203-212.
[7] Herings P J J, Van der Laan G, Talman A J J. The average tree solution for cycle-free graph games[J]. Games and Economic Behavior, 2008, 62: 77-92.
[8] Herings P J J, Van der Laan G, Talman A J J, Yang Z. The average tree solution for cooperative games with communication structure[J]. Games and Economic Behavior, 2010, 68: 626-633.
[9] Branzei R, Dimitrov D, Tijs S. Convex fuzzy games and participation monotonic allocation schemes[J]. Fuzzy Sets and Systems, 2003, 139: 267-281.
[10] Branzei R, Dimitrov D, Tijs S. Models in cooperative game theory: crisp, fuzzy and multichoice games[M]. Springer-Verlag, 2005.
[11] Tijs S, Branzei R, Ishihara S, Muto S. On cores and stable sets for fuzzy games[J]. Fuzzy Sets and Systems, 2004, 146: 285-296.
[12] Tsurumi M, Tanino T, Inuiguchi M. A Shapley function on a class of cooperative fuzzy games[J]. European Journal of Operational Research, 2001, 129: 596-618.
[13] Yu X H, Zhang Q. The fuzzy core in games with fuzzy coalitions[J]. Journal of Computational and Applied Mathematics, 2009, 230: 173-186.
[14] Aubin J P. Cooperative fuzzy games: the static and dynamic points of view[J]. Studies in Management Sciences, 1984, 20: 407-428.
[15] Mishra D, Talman A J J. A characterization of the average tree solution for tree games[J]. International Journal of Game Theory, 2010, 39: 105-111.

Profit Allocation Based on Graph Games

基于图对策的收益分配

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