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. (Games Econ. Behav. 62:77–92, 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 in J. Polit. Econ. 112:754–778, 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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Acknowledgement
For helpful comments received, the authors want to thank three anonymous referees, and the participants at the MINT 2 workshop in Saint-Etienne. Financial support by the National Agency for Research (ANR)—research program “Models of Influence and Network Theory” (MINT) ANR.09.BLANC-0321.03—and the “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) project is gratefully acknowledged.
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Béal, S., Lardon, A., Rémila, E. et al. The average tree solution for multi-choice forest games. Ann Oper Res 196, 27–51 (2012). https://doi.org/10.1007/s10479-012-1150-1
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DOI: https://doi.org/10.1007/s10479-012-1150-1