Rooted-tree solutions for tree games
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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- 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.
- Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Other publications TiSEM f243609c-2847-415f-ae52-1, Tilburg University, School of Economics and Management.
- HERINGS, P. Jean-Jacques & van der LAAN, Gerard & TALMAN, Dolf, . "The average tree solution for cycle-free graph games," CORE Discussion Papers RP 2155, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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.
- 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.
- Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the Shapley value: a new approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00178916, HAL.
- 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.
- repec:hal:journl:halshs-00178916 is not listed on IDEAS
- repec:spr:compst:v:65:y:2007:i:1:p:153-167 is not listed on IDEAS
- Mishra, D. & Talman, A.J.J., 2009.
"A Characterization of the Average Tree Solution for Cycle-Free Graph Games,"
2009-17, Tilburg University, Center for Economic Research.
- Mishra, D. & Talman, A.J.J., 2010. "A characterization of the average tree solution for cycle-free graph games," Other publications TiSEM 6cab0e52-fe09-4428-8df6-0, Tilburg University, School of Economics and Management.
- 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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