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Average tree solutions for graph games

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

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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File URL: http://mpra.ub.uni-muenchen.de/10189/1/MPRA_paper_10189.pdf
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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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  1. Herings P. Jean-Jacques & Laan Gerard van der & Talman Dolf & Yang Zaifu, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. repec:dgr:kubcen:200719 is not listed on IDEAS
  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, . "The average tree solution for cycle-free graph games," CORE Discussion Papers RP -2155, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. repec:dgr:uvatin:2008083 is not listed on IDEAS
  6. 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.
  7. Fabien Lange & Michel Grabisch, 2006. "Values on regular games under Kirchhoff's laws," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130449, HAL.
  8. repec:dgr:kubcen:200873 is not listed on IDEAS
  9. 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.
  10. repec:dgr:uvatin:20040095 is not listed on IDEAS
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