We study the additive decomposition of the Position value on hypergraph games. In 1988, Meessen considered the contributions of the links in the alliances and proposed an important allocation rule, called the Position value. By considering each conference in hypergraphs not only affects the benefit of the players in the alliances associated with it, but also affects the benefit of the players in the alliances that are not associated with it, we introduce the within groups Position value and the between groups Position value on hypergraph games to distinguish the components of each player’s benefit. We first give axiomatic characterizations for these two kinds of values. Secondly, we give an example to illustrate the within groups Position value and the between groups Position value. Finally, we propose an improved allocation rule by adjusting the proportion of the intermediary cost.
HAN Jiayu, YU Zhiqiang, ZHAO Jiagui, SHAN Erfang
. The within groups and the between groups Position values on hypergraph games[J]. Operations Research Transactions, 2022
, 26(4)
: 107
-118
.
DOI: 10.15960/j.cnki.issn.1007-6093.2022.04.009
[1] Branzei R, Dimitrov D, Tijs S. Models in Cooperative Game Theory[M].Berlin: Springer, 2008.
[2] Shapley L S. A value for n-person games[M]//Contributions to the Theory of Games II. Princeton: Princeton University Press, 1953: 307-317.
[3] Myerson R B.Graphs and cooperation in games[J]. Mathematics of Operations Research, 1977, 2(3): 225-229.
[4] Meessen R. Communication games. Nijmegen: University of Nijmegen, The Netherlands, 1988.
[5] Borm P, Owen G, Tijs S. On the position value for communication situations[J]. SIAM Journal on Discrete Mathematics, 1992, 5(3): 305-320.
[6] 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.
[7] Slikker M. A characterization of the position value[J]. International Journal of Game Theory, 2005, 33(4): 505-514.
[8] Slikker M, van den Nouweland A. Social and economic networks in cooperative game theory[J]. Theory & Decision Library, 2001, 27: 5-48.
[9] 陈纲, 张强, 冯蛟. 具有边际贡献权重的位置值[J]. 运筹与管理, 2018, 27(6): 1-5.
[10] 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.
[11] van den Brink R, Khmelnitskaya A, van den Laan G. An efficient and fair solution for communication graph games[J]. Economics Letter, 2012, 117(3): 786-789.
[12] Algaba E, Bilbao J M, Borm P, et al. The position value for union stable systems[J]. Mathematical Methods of Operations Research, 2000, 52(2): 221-236.
[13] Béal S, Rémila E, Solal P. Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions[J]. Economics Letters, 2017, 117(1): 263-267.
[14] Gómez D, González-Arangüena E, Manuel C, et al. A value for generalized probabilistic communication situations[J]. European Journal of Operational Research, 2008, 190(2): 539-556.
[15] Gómez D, González-Arangüena E, Manuel C, et al. Centrality and power in social networks: A game theoretic approach[J]. Mathematical Social Sciences, 2003, 46(1): 27-54.
[16] González-Arangüena E, Manuel C, Owen G, et al. The within groups and the between groups Myerson values[J]. European Journal of Operational Research, 2017, 257(2): 586-600.
