Characterization of the Average Tree solution and its kernel

Sylvain Béal, Eric Rémila and Philippe Solal

Journal of Mathematical Economics, 2015, vol. 60, issue C, 159-165

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 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Related works:
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)
Working Paper: Characterization of the Average Tree solution and its kernel (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:60:y:2015:i:c:p:159-165

DOI: 10.1016/j.jmateco.2015.07.001

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