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The proportional Shapley value and an application

Sylvain Béal (), Sylvain Ferrières (), Eric Rémila and Philippe Solal
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Eric Rémila: GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - UJM - Université Jean Monnet [Saint-Etienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique
Philippe Solal: GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - UJM - Université Jean Monnet [Saint-Etienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique

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Abstract: We introduce a non linear weighted Shapley value for cooperative games with transferable utility, in which the weights are endogenously given by the players' stand-alone worths. We call it the proportional Shapley value since it distributes the Harsanyi dividend (Harsanyi, 1959) of all coalitions in proportion to the stand-alone worths of its members. We show that this value recommends an appealing payoff distribution in a land production economy introduced in Shapley and Shubik (1967). Although the proportional Shapley value does not satisfy the classical axioms of linearity and consistency (Hart and Mas-Colell, 1989), the main results provide comparable axiomatic characterizations of our value and the Shapley value by means of weak versions of these two axioms. Moreover, our value inherits several well-known properties of the weighted Shapley values.

Keywords: potential; proportionality; land production economy; Harsanyi dividends; (Weighted) Shapley value (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2016-08-24
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01362228
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