Béal, Sylvain and Rémila, Eric and Solal, Philippe (2009): Average tree solutions and the distribution of Harsanyi dividends.

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Abstract
We consider communication situations games being the combination of a TUgame and a communication graph. We study the average tree (AT) solutions introduced by Herings \sl et al. [9] and [10]. The AT solutions are defined with respect to a set, say T, of rooted spanning trees of the communication graph. We characterize these solutions by efficiency, linearity and an axiom of Thierarchy. Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete.
Item Type:  MPRA Paper 

Original Title:  Average tree solutions and the distribution of Harsanyi dividends 
Language:  English 
Keywords:  Communication situations ; average tree solution ; Harsanyi solutions ; DFS ; BFS} ; Shapley value ; equal surplus division 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games 
Item ID:  17909 
Depositing User:  Sylvain Béal 
Date Deposited:  17 Oct 2009 06:27 
Last Modified:  15 Oct 2016 17:34 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/17909 