Cooperation in Dividing the Cake

CentER Discussion Paper Series No. 2008-101

22 Pages Posted: 8 Dec 2008  

Marco Dall'Aglio

LUISS Guido Carli University

Rodica Branzei

'A.l. Cuza' University of Iasi, Romania - Faculty of Computer Sciences

Stef H. Tijs

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research; Università degli Studi di Genova - Dipartimento di Matematica

Date Written: November 30, 2008

Abstract

This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players' ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.

Keywords: fair division, cooperative games, maximin partition

JEL Classification: C71, D61

Suggested Citation

Dall'Aglio, Marco and Branzei, Rodica and Tijs, Stef H., Cooperation in Dividing the Cake (November 30, 2008). CentER Discussion Paper Series No. 2008-101. Available at SSRN: https://ssrn.com/abstract=1313046 or http://dx.doi.org/10.2139/ssrn.1313046

Marco Dall'Aglio (Contact Author)

LUISS Guido Carli University

Via O. Tommasini 1
Rome, Roma 00100
Italy

Rodica Branzei

'A.l. Cuza' University of Iasi, Romania - Faculty of Computer Sciences ( email )

Carol I Blvd, Nr.11
Lasi
Romania

Stef H. Tijs

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
B925
5000 LE Tilburg
Netherlands
+31 13 466 2348 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Università degli Studi di Genova - Dipartimento di Matematica

Via Dodecaneso 35
16146 Genoa
Italy

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