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Values for transferable utility games with coalition and graph structure

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  • René Brink
  • Gerard Laan
  • Nigel Moes

Abstract

In this paper we introduce and characterize two new values for cooperative transferable utility games with graph restricted communication and a priori unions. Both values are obtained by applying the Shapley value to an associated TU-game. The graph-partition restricted TU-game is obtained by taking the Myerson graph restricted game, and of that the Kamijo partition restricted game. In this game the dividend of any coalition that is neither a subset of a union nor a union of unions is zero. The partition-graph restricted TU-game is obtained by taking the partition restricted game, and of that the graph restricted game. In this game the dividend of any coalition that is not connected in the graph is zero. We apply the values to an economic example in which the players in a union represent the cities in a country and the graph represents a network of natural gas pipelines between the cities. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • René Brink & Gerard Laan & Nigel Moes, 2015. "Values for transferable utility games with coalition and graph structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 77-99, April.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:1:p:77-99
    DOI: 10.1007/s11750-014-0324-1
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    References listed on IDEAS

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    1. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 572-589, October.
    2. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    3. Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
    4. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    6. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
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    Cited by:

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    2. Zijun Li & Fanyong Meng, 2023. "The α-Egalitarian Myerson value of games with communication structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 311-338, June.
    3. Zhang, Guang, 2018. "Allocation rules for cooperative games with graph and hypergraph communication structure," Other publications TiSEM 10431594-5325-4503-bdb0-0, Tilburg University, School of Economics and Management.
    4. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    5. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    6. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2020. "On egalitarian values for cooperative games with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 672-688, October.

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