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The Average Tree Solution for Multi-choice Forest Games

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

Abstract

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 28739.

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Date of creation: 08 Feb 2011
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Handle: RePEc:pra:mprapa:28739

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Keywords: Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.;

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References

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  1. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
  2. 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.
  3. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377604, Tilburg University.
  4. Ren� van den Brink, 2009. "Comparable Axiomatizations of the Myerson Value, the Restricted Banzhaf Value, Hierarchical Outcomes and the Average Tree Solution for Cycle-Free Graph Restricted Games," Tinbergen Institute Discussion Papers 09-108/1, Tinbergen Institute.
  5. Michel Grabisch & Lijue Xie, 2007. "A new approach to the core and Weber set of multichoice games," Computational Statistics, Springer, vol. 66(3), pages 491-512, December.
  6. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer, vol. 21(4), pages 351-60.
  7. 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.
  8. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Computational Statistics, Springer, vol. 65(1), pages 153-167, February.
  9. Nouweland, C.G.A.M.. van den & Potters, J. & Tijs, S.H. & Zarzuelo, J., 1991. "Cores and related solution concepts for multi-choice games," Research Memorandum 478, Tilburg University, Faculty of Economics and Business Administration.
  10. 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.
  11. José Zarzuelo & Marco Slikker & Flip Klijn, 1999. "Characterizations of a multi-choice value," International Journal of Game Theory, Springer, vol. 28(4), pages 521-532.
  12. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  13. Albizuri, M.J. & Aurrecoechea, J. & Zarzuelo, J.M., 2006. "Configuration values: Extensions of the coalitional Owen value," Games and Economic Behavior, Elsevier, vol. 57(1), pages 1-17, October.
  14. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
  15. Hwang, Yan-An & Liao, Yu-Hsien, 2008. "Potential approach and characterizations of a Shapley value in multi-choice games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 321-335, November.
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Cited by:
  1. Brink, R. van den & Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2013. "The Average Tree Permission Value for Games with a Permission Tree," Discussion Paper 2013-001, Tilburg University, Center for Economic Research.

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