The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure
AbstractThe 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 144 (2009)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/inca/622869
Coalition structure Externalities Partition function games Recursion Shapley value;
Other versions of this item:
- McQuillin, Ben, 2008. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," MPRA Paper 12049, University Library of Munich, Germany.
- D62 - Microeconomics - - Welfare Economics - - - Externalities
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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