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The average tree solution for cooperative games with communication structure

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Author Info

  • Herings, P.J.J.

    (Tilburg University)

  • Laan, G. van der
  • Talman, A.J.J.

    (Tilburg University)

  • Yang, Z.F.

    (Tilburg University)

Abstract

We study cooperative games with communication structure, represented by an undirectedgraph. Players in the game are able to cooperate only if they can form a network in the graph. A single-valued solution, the average tree solution, is proposed for this class ofgames. Given the graph structure we define a collection of spanning trees, where eachspanning tree specifies a particular way by which players communicate and determines a payoff vector of marginal contributions of all the players. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has acomplete communication structure, then the proposed solution coincides with the Shapleyvalue, and that if the game has a cycle-free communication structure, it is the solutionproposed by Herings, van der Laan and Talman (2008). We introduce the notion of linkconvexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link-convexity is weaker than convexity. For games with a cycle-free communication structure, link-convexity is even weaker than super-additivity.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-3736837.

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Date of creation: 2010
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Publication status: Published in Games and Economic Behavior (2010) v.68, p.626-633
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-3736837

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Web page: http://www.tilburguniversity.edu/

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  1. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
  2. 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).
  3. repec:dgr:uvatin:2004095 is not listed on IDEAS
  4. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
  5. Talman, A.J.J. & Yamamoto, Y., 2008. "Average tree solution and subcore for acyclic graph games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3129818, Tilburg University.
  6. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  7. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  8. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  9. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer, vol. 40(1), pages 87-110, February.
  10. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research.
  11. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  12. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
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Cited by:
  1. Huseynov, T. & Talman, A.J.J., 2012. "The Communication Tree Value for TU-games with Graph Communication," Discussion Paper 2012-095, Tilburg University, Center for Economic Research.
  2. repec:dgr:uvatin:2012050 is not listed on IDEAS
  3. Koshevoy, Gleb & Talman, Dolf, 2014. "Solution concepts for games with general coalitional structure," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 19-30.
  4. Khmelnitskaya, A. & Selcuk, O. & Talman, A.J.J., 2012. "The Average Covering Tree Value for Directed Graph Games," Discussion Paper 2012-037, Tilburg University, Center for Economic Research.
  5. Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Compensations in the Shapley value and the compensation solutions for graph games," International Journal of Game Theory, Springer, vol. 41(1), pages 157-178, February.
  6. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
  7. Khmelnitskaya, Anna B. & Sudhölter, Peter, 2011. "The prenucleolus for games with communication structures," Discussion Papers of Business and Economics 10/2011, Department of Business and Economics, University of Southern Denmark.
  8. S. Ryuo & K. Sato & Y. Yamamoto, 2012. "Parameterized fairness axioms on cycle-free graph games," Journal of Global Optimization, Springer, vol. 52(3), pages 487-497, March.
  9. Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper 2011-119, Tilburg University, Center for Economic Research.
  10. Albizuri, M. Josune & Sudhölter, Peter, 2014. "On the Core of Games with Communication Structures," Discussion Papers of Business and Economics 6/2014, Department of Business and Economics, University of Southern Denmark.
  11. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2013. "Solutions For Games With General Coalitional Structure And Choice Sets," Discussion Paper 2013-012, Tilburg University, Center for Economic Research.
  12. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
  13. Napel, Stefan & Nohn, Andreas & Alonso-Meijide, José Maria, 2012. "Monotonicity of power in weighted voting games with restricted communication," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 247-257.
  14. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
  15. repec:pdn:wpaper:73 is not listed on IDEAS
  16. Selçuk, Özer & Suzuki, Takamasa & Talman, Dolf, 2013. "Equivalence and axiomatization of solutions for cooperative games with circular communication structure," Economics Letters, Elsevier, vol. 121(3), pages 428-431.
  17. Suzuki, T. & Talman, A.J.J., 2011. "Solution Concepts for Cooperative Games with Circular Communication Structure," Discussion Paper 2011-100, Tilburg University, Center for Economic Research.
  18. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Average tree solutions and the distribution of Harsanyi dividends," MPRA Paper 17909, University Library of Munich, Germany.

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