### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 25 |

Volume | 2001-33 |

Publication status | Published - 2001 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2001-33 |

### Fingerprint

### Keywords

- game theory

### Cite this

*A Class of Consistent Share Functions For Games in Coalition Structure*. (CentER Discussion Paper; Vol. 2001-33). Tilburg: Microeconomics.

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - A Class of Consistent Share Functions For Games in Coalition Structure

AU - van den Brink, J.R.

AU - van der Laan, G.

N1 - Pagination: 25

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - game theory

M3 - Discussion paper

VL - 2001-33

T3 - CentER Discussion Paper

BT - A Class of Consistent Share Functions For Games in Coalition Structure

PB - Microeconomics

CY - Tilburg

ER -