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Core concepts for share vectors

Listed author(s):
  • Gerard van der Laan


    (Department of Econometrics and Tinbergen Institute, Free University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

  • René van den Brink


    (Department of Econometrics and Center, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

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.

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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 18 (2001)
Issue (Month): 4 ()
Pages: 759-784

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Handle: RePEc:spr:sochwe:v:18:y:2001:i:4:p:759-784
Note: Received: 9 August 1999/Accepted: 25 April 2000
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