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The average tree solution for cooperative games with communication structure

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  • Herings, P.J.J.
  • van der Laan, G.
  • Talman, A.J.J.
  • Yang, Z.

Abstract

We study cooperative games with communication structure, represented by an undirected graph. 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 of games. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has a complete communication structure, then the proposed solution coincides with the Shapley value, and that if the game has a cycle-free communication structure, it is the solution proposed by Herings, van der Laan and Talman in 2008. We introduce the notion of link-convexity, 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

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 68 (2010)
Issue (Month): 2 (March)
Pages: 626-633

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Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:626-633

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Cooperative game Graph structure Single-valued solution Core Convexity Spanning tree;

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  1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, Springer, vol. 33(4), pages 505-514, November.
  2. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 112(4), pages 754-778, August.
  3. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 620, Cowles Foundation for Research in Economics, Yale University.
  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, Elsevier, vol. 62(1), pages 77-92, January.
  5. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, Springer, vol. 20(4), pages 419-27.
  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. 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.
  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. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper, Tilburg University, Center for Economic Research 2007-19, Tilburg University, Center for Economic Research.
  10. 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.
  11. Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers, DELTA (Ecole normale supérieure) 91-16, DELTA (Ecole normale supérieure).
  12. 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.
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Citations

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Cited by:
  1. Richard Baron & Sylvain Béal & Eric Rémila & Philippe Solal, 2011. "Average tree solutions and the distribution of Harsanyi dividends," International Journal of Game Theory, Springer, Springer, vol. 40(2), pages 331-349, May.
  2. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2012. "A Strategic Implementation of the Average Tree Solution for Cycle-Free Graph Games," Tinbergen Institute Discussion Papers 12-050/1, Tinbergen Institute.
  3. Koshevoy, Gleb & Talman, Dolf, 2014. "Solution concepts for games with general coalitional structure," Mathematical Social Sciences, Elsevier, Elsevier, vol. 68(C), pages 19-30.
  4. Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper, Tilburg University, Center for Economic Research 2011-119, Tilburg University, Center for Economic Research.
  5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Weighted Component Fairness for Forest Games," MPRA Paper 17455, University Library of Munich, Germany.
  6. Suzuki, T. & Talman, A.J.J., 2011. "Solution Concepts for Cooperative Games with Circular Communication Structure," Discussion Paper, Tilburg University, Center for Economic Research 2011-100, Tilburg University, Center for Economic Research.
  7. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Compensations in the Shapley value and the compensation solutions for graph games," MPRA Paper 20955, University Library of Munich, Germany.
  8. 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.
  9. 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.
  10. Huseynov, T. & Talman, A.J.J., 2012. "The Communication Tree Value for TU-games with Graph Communication," Discussion Paper, Tilburg University, Center for Economic Research 2012-095, Tilburg University, Center for Economic Research.
  11. 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, Elsevier, vol. 148(6), pages 2737-2748.
  12. Khmelnitskaya, A. & Selcuk, O. & Talman, A.J.J., 2012. "The Average Covering Tree Value for Directed Graph Games," Discussion Paper, Tilburg University, Center for Economic Research 2012-037, Tilburg University, Center for Economic Research.
  13. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2013. "Solutions For Games With General Coalitional Structure And Choice Sets," Discussion Paper, Tilburg University, Center for Economic Research 2013-012, Tilburg University, Center for Economic Research.
  14. Napel, Stefan & Nohn, Andreas & Alonso-Meijide, José Maria, 2012. "Monotonicity of power in weighted voting games with restricted communication," Mathematical Social Sciences, Elsevier, Elsevier, vol. 64(3), pages 247-257.
  15. S. Ryuo & K. Sato & Y. Yamamoto, 2012. "Parameterized fairness axioms on cycle-free graph games," Journal of Global Optimization, Springer, Springer, vol. 52(3), pages 487-497, March.
  16. 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.
  17. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
  18. repec:pdn:wpaper:73 is not listed on IDEAS

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