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Average tree solutions for graph games

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Author Info

  • Baron, Richard
  • Béal, Sylvain
  • Remila, Eric
  • Solal, Philippe

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10189.

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Date of creation: 31 Jul 2008
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Handle: RePEc:pra:mprapa:10189

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References

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  1. Fabien Lange & Michel Grabisch, 2006. "Values on regular games under Kirchhoff's laws," Cahiers de la Maison des Sciences Economiques b06087, Université Panthéon-Sorbonne (Paris 1).
  2. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2010. "The average tree solution for cooperative games with communication structure," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3736837, Tilburg University.
  3. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
  4. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
  5. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, vol. 33(2), pages 349-364, November.
  6. repec:dgr:uvatin:2008083 is not listed on IDEAS
  7. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research.
  8. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
  9. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
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Cited by:
  1. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  2. 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.
  3. repec:dgr:uvatin:2008083 is not listed on IDEAS

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