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A Class of Consistent Share Functions for Games in Coalition Structure

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Author Info
René van den Brink () (Tilburg University)
Gerard van der Laan () (Vrije Universiteit Amsterdam)

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Abstract

A cooperative game with transferable utility describes a situation in which players can obtain certain payoffs by cooperation. A share function for such games is a function which assigns for every game a distribution of the payoffs over the players in the game.

In this paper we consider cooperative games in which the players are organized into an a priori coalition structure being a finite partition of the set of players. We introduce a general method for defining a class of share functions for such games in coalition structure using a multiplication property that states that the share of a player in the total payoff is equal to its share in some internal game within its coalition multiplied by the share of this coalition in an external game between the coalitions. We show that these coalition structure share functions satisfy certain consistency properties. We provide axiomatizations of this class of coalition structure share functions using these consistency and multiplication properties.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-044/1.

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Date of creation: 27 Apr 2001
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Handle: RePEc:dgr:uvatin:20010044

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: TU-Game coalition structure share function multiplication property consistency

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  2. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July. [Downloadable!] (restricted)
  3. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  4. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582. [Downloadable!] (restricted)
  5. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer, vol. 18(2), pages 227-40.
  6. René van den Brink & Gerard van der Laan, 1999. "Core Concepts for Share Vectors," Tinbergen Institute Discussion Papers 99-057/1, Tinbergen Institute.
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  7. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer, vol. 28(4), pages 547-565. [Downloadable!] (restricted)
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  8. René van den Brink & Gerard van der Laan, 1998. "The Normalized Banzhaf Value and the Banzhaf Share Function," Tinbergen Institute Discussion Papers 98-042/1, Tinbergen Institute.
  9. Gerard van der Laan & René van den Brink, 1998. "A Banzhaf Share Function for Cooperative Games in Coalition Structure," Tinbergen Institute Discussion Papers 98-043/1, Tinbergen Institute.
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