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Characterization of the Average Tree solution and its kernel

Institution:	1. Université de Franche-Comté, CRESE, 30 Avenue de l’Observatoire, 25009 Besançon, France;2. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France;1. Department of Economics, University of Rochester, Rochester, NY 14627, USA;2. Department of Economics, Vanderbilt University, Nashville, TN 37235, USA;3. College of Administrative Sciences and Economics, Koç University, Sar?yer, Istanbul, 34450, Turkey;1. School of Economics, UNSW Australia, Sydney, NSW 2052, Australia;2. Business Intelligence and Smart Services Institute, Maastricht University, Maastricht, The Netherlands;1. UMR CNRS 7285, IC2MP, Bâtiment B35, 5, Avenue Albert Turpain, 86022 Poitiers cedex, France;2. UMR 6118, département Géosciences, Université de Rennes, 35042 Rennes, France;3. UMR 7517 CNRS, Laboratoire d’Hydrologie et de Géochimie de Strasbourg, 1 rue Blessig 67082, Strasbourg cedex, France;4. Clermont Université, Université Blaise Pascal, Laboratoire Magmas et Volcans, BP 10448, F-63000 Clermont-Ferrand, France;5. CNRS, UMR 6524, LMV, F-63038 Clermont-Ferrand, France;6. IRD, R 163, LMV, F-63038 Clermont-Ferrand, France;7. GeoRessources UMR 7359, BP 239, F-54506 Vandoeuvre les Nancy, France

Abstract:	In this article, 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 first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new basis for these spaces of TU-games. We then focus our attention on the Average (rooted)-Tree solution (see Herings et al. (2008)). We provide a basis for its kernel and a new axiomatic characterization by using the classical axiom for inessential games, and two new axioms of invariance called Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions. We also solve the inverse problem for the Average (rooted)-Tree solution.

Keywords:	Average Tree solution Direct-sum decomposition Kernel Weighted addition invariance on bi-partitions Invariance to irrelevant coalitions Inverse problem
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