Axiomatization and Implementation of Discounted Shapley Values

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper we introduce discounting in the bidding mechanism of Pérez-Castrillo and Wettstein (J Econ Theory 100:274–294, 2001) who implemented the Shapley value for cooperative transferable utility games. This modification of the mechanism yields the corresponding discounted Shapley value as the payoff distribution in every subgame perfect equilibrium. The class of discounted Shapley values contains the Shapley value and equal division solution as its extreme cases. Interestingly, we obtain axiomatizations of each solution in this class by generalizing the null player property (of the Shapley value) and nullifying player property (of the equal division solution) to the so-called δ-reducing player property.
Original languageEnglish
Pages (from-to)329-344
JournalSocial Choice and Welfare
Volume45
Issue number2
Early online date5 Jun 2015
DOIs
Publication statusPublished - 2015

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title = "Axiomatization and Implementation of Discounted Shapley Values",
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Axiomatization and Implementation of Discounted Shapley Values. / van den Brink, J.R.; Funaki, Y.

In: Social Choice and Welfare, Vol. 45, No. 2, 2015, p. 329-344.

Research output: Contribution to JournalArticleAcademicpeer-review

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AB - In this paper we introduce discounting in the bidding mechanism of Pérez-Castrillo and Wettstein (J Econ Theory 100:274–294, 2001) who implemented the Shapley value for cooperative transferable utility games. This modification of the mechanism yields the corresponding discounted Shapley value as the payoff distribution in every subgame perfect equilibrium. The class of discounted Shapley values contains the Shapley value and equal division solution as its extreme cases. Interestingly, we obtain axiomatizations of each solution in this class by generalizing the null player property (of the Shapley value) and nullifying player property (of the equal division solution) to the so-called δ-reducing player property.

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DO - 10.1007/s00355-015-0899-y

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