Coalition-weighted Shapley values

Estela Sánchez-Rodríguez (), Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo and Iago Núñez Lugilde
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Estela Sánchez-Rodríguez: Universidade de Vigo
Miguel Ángel Mirás Calvo: Universidade de Vigo
Carmen Quinteiro Sandomingo: Universidade de Vigo
Iago Núñez Lugilde: Universidade de Vigo

International Journal of Game Theory, 2024, vol. 53, issue 2, No 11, 547-577

Abstract: Abstract We introduce a new class of values for coalitional games: the coalition-weighted Shapley values. Weights can be assigned to coalitions, not just to players, and zero-weights are admissible. The Shapley value belongs to this class. Coalition-weighted Shapley values recommend for each game the allocation defined by the Shapley value of a weighted game obtained as a linear convex combination of the associated marginal games. Coalition-weighted Shapley values are random order values and Harsanyi values. Positively weighted Shapley values and weighted Shapley values can be seen as the limit of a sequence of iterated coalition-weighted Shapley values. We provide axiomatic characterizations of coalition-weighted Shapley values through properties that do not involve the weights. Finally, we discuss how to extend our model to include exogenous coalition structures as in the hierarchical and Owen values.

Keywords: Shapley value; Weighted Shapley values; Marginal games; Characterization of values; Coalition structure (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-023-00877-w

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