Average tree solutions and the distribution of Harsanyi dividends

Average tree solutions and the distribution of Harsanyi dividends

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Article ID: iaor20116136
Volume: 40
Issue: 2
Start Page Number: 331
End Page Number: 349
Publication Date: May 2011
Journal: International Journal of Game Theory
Authors: , , ,
Keywords: communication, graphs
Abstract:

We consider communication situations games being the combination of a TU‐game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al. (2008, 2010). The AT solutions are defined with respect to a set, say fancyscript T equ1 , of rooted spanning trees of the communication graph. We prove the following results. Firstly, the AT solution with respect to fancyscript T equ2 is a Harsanyi solution if and only if fancyscript T equ3 is a subset of the set of trees introduced in Herings et al. (2010). 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.

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