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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," Discussion Papers 09-08, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:09-08
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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.
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    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
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    7. 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. 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.
    2. Richard Baron & Sylvain Béal & Eric Rémila & Philippe Solal, 2011. "Average tree solutions and the distribution of Harsanyi dividends," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 331-349, May.
    3. 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.
    4. 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.
    5. Suzuki, T. & Talman, A.J.J., 2011. "Solution Concepts for Cooperative Games with Circular Communication Structure," Discussion Paper 2011-100, Tilburg University, Center for Economic Research.
    6. Sylvain Béal & Eric Rémila & Philippe Solal, 2022. "Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 818-849, May.
    7. Özer Selçuk & Takamasa Suzuki, 2023. "Comparable axiomatizations of the average tree solution and the Myerson value," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 333-362, June.
    8. 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.
    9. 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.
    10. Liying Kang & Anna Khmelnitskaya & Erfang Shan & Dolf Talman & Guang Zhang, 2023. "The two-step average tree value for graph and hypergraph games," Annals of Operations Research, Springer, vol. 323(1), pages 109-129, April.
    11. 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.
    12. Liying Kang & Anna Khmelnitskaya & Erfang Shan & Dolf Talman & Guang Zhang, 2021. "The average tree value for hypergraph games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 437-460, December.
    13. 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.
    14. 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.

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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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