Characterization of the Average Tree solution and its kernel

Sylvain Béal, Eric Rémila and Philippe Solal

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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, P., van der Laan, G., Talman, D., 2008. The Average Tree Solution for Cycle-free Games. Games and Economic Behavior 62, 77-92). 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, namely Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions.

Keywords: Average Tree solution; Direct-sum decomposition; Kernel; Weighted addition; invariance on bi-partitions; Invariance to irrelevant coalitions (search for similar items in EconPapers)
Date: 2014-11-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01377928v1
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Related works:
Journal Article: Characterization of the Average Tree solution and its kernel (2015)
Working Paper: Characterization of the Average Tree solution and its kernel (2015)
Working Paper: Characterization of the Average Tree solution and its kernel (2015)
Working Paper: Characterization of the Average Tree solution and its kernel (2014)
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