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Two Values for Transferable Utility Games with Coalition and Graph Structure

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  • Rene van den Brink

    (VU University Amsterdam)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Nigel Moes

    (VU University Amsterdam)

Abstract

In this paper we introduce and characterize two new values for transferable utility games with graph restricted communication and a priori unions. Both values are obtained by applying the Shapley value to an associated TU-game. The graph-partition restricted TU-game is obtained by taking the Myerson graph restricted game and of that the Kamijo partition restricted game. In this game the dividend of any coalition that is neither a subset of a union nor a union of unions is zero. The partition-graph restricted TU-game is obtained by taking the partition restricted game and of that the graph restricted game. In this game the dividend of any coalition that is not connected in the graph is zero. We apply the values to an economic example in which the players in a union represent the cities in a country and the graph represents a network of natural gas pipelines between the cities.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-164/1.

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Date of creation: 16 Nov 2011
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Handle: RePEc:dgr:uvatin:20110164

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Related research

Keywords: cooperative games; coalition structures; graphs; Shapley value;

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  1. 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.
  2. Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
  3. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(3), pages 572-589, October.
  4. van den Brink, Rene & van der Laan, Gerard, 2005. "A class of consistent share functions for games in coalition structure," Games and Economic Behavior, Elsevier, vol. 51(1), pages 193-212, April.
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