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A Characterization of the average tree solution for tree games

Author

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  • Debasis Mishra

    () (Indian Statistical Institute, New Delhi)

  • Dolf Talman

    (Tilburg University)

Abstract

For the class of tree games, a new solution called the average tree solution has been proposed recently. We provide a characterization of this solution. This characterization underlines an important difference, in terms of symmetric treatment of the agents, between the average tree solution and the Myerson value for the class of tree games.

Suggested Citation

  • Debasis Mishra & Dolf Talman, 2009. "A Characterization of the average tree solution for tree games," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 09-08, Indian Statistical Institute, New Delhi, India.
  • Handle: RePEc:ind:isipdp:09-08
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    File URL: http://www.isid.ac.in/~pu/dispapers/dp09-08.pdf
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    References listed on IDEAS

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    1. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    2. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
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    4. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    5. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    6. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
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    Citations

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    Cited by:

    1. M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
    3. S. Béal & A. Lardon & E. Rémila & P. Solal, 2012. "The average tree solution for multi-choice forest games," Annals of Operations Research, Springer, vol. 196(1), pages 27-51, July.
    4. Kang, Liying & Khmelnitskaya, Anna & Shan, Erfang & Talman, A.J.J. & Zhang, Guang, 2020. "The Average Tree value for Hypergraph Games," Other publications TiSEM 331f101b-09ee-47d6-afdf-e, Tilburg University, School of Economics and Management.
    5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Characterization of the Average Tree solution and its kernel," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 159-165.
    6. Suzuki, T. & Talman, A.J.J., 2011. "Solution Concepts for Cooperative Games with Circular Communication Structure," Other publications TiSEM d863606f-a58a-4f92-894d-e, Tilburg University, School of Economics and Management.
    7. Anna Khmelnitskaya & Gerard van der Laan & Dolf Talman, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Tinbergen Institute Discussion Papers 16-070/II, Tinbergen Institute.
    8. J. R. Fernández & I. Gallego & A. Jiménez-Losada & M. Ordóñez, 2019. "The cg-average tree value for games on cycle-free fuzzy communication structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 456-478, October.
    9. Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper 2011-119, Tilburg University, Center for Economic Research.
    10. Selçuk, Özer & Suzuki, Takamasa & Talman, Dolf, 2013. "Equivalence and axiomatization of solutions for cooperative games with circular communication structure," Economics Letters, Elsevier, vol. 121(3), pages 428-431.

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    More about this item

    Keywords

    tree; graph games; Myerson value; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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