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An Owen-Type Value for Games with Two-Level Communication Structures

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  • Rene van den Brink

    (VU University Amsterdam)

  • Anna Khmelnitskaya

    (Saint-Petersburg State University)

  • Gerard van der Laan

    (VU University Amsterdam)

Abstract

We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph, so there is a communication graph between the unions of the coalition structure as well as a communication graph on the players in every union. We also show that, for particular two-level communication structures, the Owen value and the Aumann-Dreze value for games with coalition structures, the Myerson value for communication graph games and the equal surplus division solution appear as special cases of this new value.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-089/1.

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Date of creation: 11 Jun 2011
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Handle: RePEc:dgr:uvatin:20110089

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Web page: http://www.tinbergen.nl

Related research

Keywords: TU game; coalition structure; communication graph; Owen value; Myerson value;

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References

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  1. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
  2. Brink, J.R. van den & Laan, G. van der, 2001. "A Class of Consistent Share Functions For Games in Coalition Structure," Discussion Paper 2001-33, Tilburg University, Center for Economic Research.
  3. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
  4. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
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