Hodge decomposition and the Shapley value of a cooperative game

Ari Stern and Alexander Tettenhorst

Games and Economic Behavior, 2019, vol. 113, issue C, 186-198

Abstract: We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry, and linearity properties. Consequently, we obtain a new characterization of the classical Shapley value as the value of the grand coalition in each player's component game. We also relate this decomposition to a least-squares problem involving inessential games (in a similar spirit to previous work on least-squares and minimum-norm solution concepts) and to the graph Laplacian. Finally, we generalize this approach to games with weights and/or constraints on coalition formation.

Keywords: Shapley value; Cooperative game theory; Hodge decomposition; Graph Laplacian (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:113:y:2019:i:c:p:186-198

DOI: 10.1016/j.geb.2018.09.006

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