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Average tree solutions for graph games

Author

Listed:
  • Richard Baron

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Sylvain Béal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Éric Rémila

    (LIP - Laboratoire de l'Informatique du Parallélisme - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - Inria - Institut National de Recherche en Informatique et en Automatique - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

Abstract

In this paper we consider cooperative graph games being TU-games in which players cooperate if they are connected in the communication graph. We focus our attention to the average tree solutions introduced by Herings, van der Laan and Talman [6] and Herings, van der Laan, Talman and Yang [7]. Each average tree solution is defined with re- spect to a set, say T , of admissible rooted spanning trees. Each average tree solution is characterized by efficiency, linearity and an axiom of T - hierarchy on the class of all graph games with a fixed communication graph. We also establish that the set of admissible rooted spanning trees introduced by Herings, van der Laan, Talman and Yang [7] is the largest set of rooted spanning trees such that the corresponding aver- age tree solution is a Harsanyi solution. One the other hand, we show that this set of rooted spanning trees cannot be constructed by a dis- tributed algorithm. Finally, we propose a larger set of spanning trees which coincides with the set of all rooted spanning trees in clique-free graphs and that can be computed by a distributed algorithm.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Richard Baron & Sylvain Béal & Éric Rémila & Philippe Solal, 2008. "Average tree solutions for graph games," Post-Print hal-00332570, HAL.
    • Handle: RePEc:hal:journl:hal-00332570
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    Cited by:

    1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010. "The average tree solution for cooperative games with communication structure," Games and Economic Behavior, Elsevier, vol. 68(2), pages 626-633, March.
    2. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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