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Rooted-tree solutions for tree games

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

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00531-1
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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 203 (2010)
Issue (Month): 2 (June)
Pages: 404-408

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Handle: RePEc:eee:ejores:v:203:y:2010:i:2:p:404-408
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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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, vol. 39(1), pages 105-111, March.
  3. 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), vol. 65(1), pages 153-167, February.
  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. repec:hal:journl:halshs-00178916 is not listed on IDEAS
  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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