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The proportional Shapley value and an application

Authors
  • Béal, Sylvain
  • Ferrières, Sylvain
  • Rémila, Eric
  • Solal, Philippe
Publication Date
Aug 24, 2016
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
External links

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.

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