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The proportional Shapley value and an application

Sylvain Béal (), Sylvain Ferrières (), Eric Rémila () and Phillippe Solal ()
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Eric Rémila: Université de Saint-Etienne, Gate
Phillippe Solal: Université de Saint-Etienne, Gate

No 2016-08, Working Papers from CRESE

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 theproportional 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: (Weighted) Shapley value; proportionality; Harsanyi dividends; potential; land production economy (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-mic
Date: 2016-08
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