Core concepts for share vectors

Gerard van der Laan and Rene van den Brink ()

Social Choice and Welfare, 2001, vol. 18, issue 4, 759-784

Abstract: A value mapping for cooperative games with transferable utilities is a mapping that assigns to every game a set of vectors each representing a distribution of the payoffs. A value mapping is efficient if to every game it assigns a set of vectors which components all sum up to the worth that can be obtained by all players cooperating together. An approach to efficiently allocate the worth of the `grand coalition' is using share mappings which assign to every game a set of share vectors being vectors which components sum up to one. Every component of a share vector is the corresponding players' share in the total payoff that is to be distributed among the players. In this paper we discuss a class of share mappings containing the (Shapley) share-core, the Banzhaf share-core and the Large Banzhaf share-core, and provide characterizations of this class of share mappings.

Date: 2001-10-08
Note: Received: 9 August 1999/Accepted: 25 April 2000
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