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Games With Limited Communication Structure

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  • Talman, A.J.J.
  • Yamamoto, Y.

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average tree solution has been proposed. It was proven that the average tree solution is a core element if the game exhibits superadditivity. It will be shown that the condition of super-additivity can be relaxed to a weaker condition, which admits for a natural interpretation. Moreover, the concept of subcore is introduced. Under the same condition it is proven that the subcore is a subset of the core and always contains the average tree solution and therefore is a non-empty refinement of the core.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-19.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200719

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References

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  1. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  2. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  5. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, vol. 20(4), pages 419-27.
  6. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2005. "The Component Fairness Solution for Cycle-Free Graph Games," Discussion Paper 2005-127, Tilburg University, Center for Economic Research.
  7. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  8. 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.
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Cited by:
  1. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Tinbergen Institute Discussion Papers 08-083/1, Tinbergen Institute.
  2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
  3. 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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