Journal
JOURNAL OF ECONOMIC THEORY
Volume 144, Issue 2, Pages 696-721Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jet.2008.05.010
Keywords
Coalition structure; Externalities; Partition function games; Recursion; Shapley value
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Funding
- ESRC [RES-051-27-0146] Funding Source: UKRI
- Economic and Social Research Council [RES-051-27-0146] Funding Source: researchfish
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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. (C) 2008 Elsevier Inc. All rights reserved.
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