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Rooted-tree solutions for tree games

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  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe

Abstract

In this paper, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We introduce natural extensions of the average (rooted)-tree solution (see [Herings, P., van der Laan, G., Talman, D., 2008. The average tree solution for cycle free games. Games and Economic Behavior 62, 77-92]): the marginalist tree solutions and the random tree solutions. We provide an axiomatic characterization of each of these sets of solutions. By the way, we obtain a new characterization of the average tree solution.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:203:y:2010:i:2:p:404-408
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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. Debasis Mishra & A. Talman, 2010. "A characterization of the average tree solution for tree games," International Journal of Game Theory, Springer;Game Theory Society, pages 105-111.
    3. repec:hal:journl:halshs-00178916 is not listed on IDEAS
    4. 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.
    5. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), pages 153-167.
    6. repec:spr:compst:v:65:y:2007:i:1:p:153-167 is not listed on IDEAS
    7. Mishra, D. & Talman, A.J.J., 2009. "A Characterization of the Average Tree Solution for Cycle-Free Graph Games," Discussion Paper 2009-17, Tilburg University, Center for Economic Research.
    8. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
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    Citations

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    Cited by:

    1. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, pages 33-64.
    2. 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.
    3. 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.
    4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, pages 144-151.
    5. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    6. Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Compensations in the Shapley value and the compensation solutions for graph games," International Journal of Game Theory, Springer;Game Theory Society, pages 157-178.
    7. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, pages 709-717.
    8. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    9. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
    10. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
    11. Sylvain Béal & Eric Rémila & Phillippe Solal, 2015. "Discounted Tree Solutions," Working Papers 2015-18, CRESE.
    12. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Characterization of the Average Tree solution and its kernel," Journal of Mathematical Economics, Elsevier, pages 159-165.
    13. repec:hal:cesptp:halshs-00950109 is not listed on IDEAS
    14. Khmelnitskaya, Anna & Talman, Dolf, 2014. "Tree, web and average web values for cycle-free directed graph games," European Journal of Operational Research, Elsevier, vol. 235(1), pages 233-246.
    15. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2012. "The Sequential Equal Surplus Division for Sharing International Rivers with Bifurcations," Working Papers 2012-02, CRESE.
    16. González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    17. repec:hal:cesptp:hal-00803233 is not listed on IDEAS

    More about this item

    Keywords

    C71 Average tree solution Communication structure Marginal contributions Random (order) values;

    JEL classification:

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

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