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The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

  • McQuillin, Ben

The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a "partition function" outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show that simultaneous consideration of the two elaborations ("generalization" and "extension") obtains a unique Shapley-type value for games in partition function form. The key requirement is that the "Extended, Generalized Shapley Value" (EGSV) should be "recursive": the EGSV of any game should be the EGSV of itself. This requirement forces us to ignore all but the payoffs to bilateral partitions. The EGSV can be conceptualized as the ex ante value of a process of successive bilateral amalgamations. Previous Shapley value extensions, if generalized, are not recursive; indeed, they iterate to the EGSV.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 2 (March)
Pages: 696-721

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:696-721
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Debraj Ray & Rajiv Vohra, 1996. "A Theory of Endogenous Coalition Structure," Papers 0068, Boston University - Industry Studies Programme.
  2. Kim Hang Pham Do & Henk Norde, 2007. "The Shapley Value For Partition Function Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 353-360.
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  5. Geoffroy de Clippel & Roberto Serrano, 2007. "Marginal contributions and externalities in the value," Working Papers 2007-04, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  6. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
  7. Salant, Stephen W & Switzer, Sheldon & Reynolds, Robert J, 1983. "Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 185-99, May.
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