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

McQuillin, Ben (2008): The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure. Forthcoming in: Journal of Economic Theory

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Coalition structure; Externalities; Partition function games; Recursion; Shapley value
• Subjects: D - Microeconomics > D6 - Welfare Economics > D62 - Externalities; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

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