A Class of Consistent Share Functions For Games in Coalition Structure

J.R. van den Brink, G. van der Laan

Research output: Working paperDiscussion paperOther research output

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Abstract

A cooperative game with transferable utility -or simply a TU-game- describes a situation in which players can obtain certain payoffs by cooperation.A value function for these games is a function which assigns to every such a game a distribution of the payoffs over the players in the game.An alternative type of solutions are share functions which assign to every player in a TU-game its share in the payoffs to be distributed.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 player i in the total payoff is equal to the share of player i in some internal game within i 's a priori coalition, multiplied by the share of this coalition in an external game between the a priori given 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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages25
Volume2001-33
Publication statusPublished - 2001

Publication series

NameCentER Discussion Paper
Volume2001-33

Fingerprint

Coalition structure
TU game
Cooperative game
Axiomatization
Transferable utility
Value function

Keywords

  • game theory

Cite this

van den Brink, J. R., & van der Laan, G. (2001). A Class of Consistent Share Functions For Games in Coalition Structure. (CentER Discussion Paper; Vol. 2001-33). Tilburg: Microeconomics.
van den Brink, J.R. ; van der Laan, G. / A Class of Consistent Share Functions For Games in Coalition Structure. Tilburg : Microeconomics, 2001. (CentER Discussion Paper).
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van den Brink, JR & van der Laan, G 2001 'A Class of Consistent Share Functions For Games in Coalition Structure' CentER Discussion Paper, vol. 2001-33, Microeconomics, Tilburg.

A Class of Consistent Share Functions For Games in Coalition Structure. / van den Brink, J.R.; van der Laan, G.

Tilburg : Microeconomics, 2001. (CentER Discussion Paper; Vol. 2001-33).

Research output: Working paperDiscussion paperOther research output

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van den Brink JR, van der Laan G. A Class of Consistent Share Functions For Games in Coalition Structure. Tilburg: Microeconomics. 2001. (CentER Discussion Paper).