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Cooperation in Dividing the Cake

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  • Dall'Aglio, M.
  • Brânzei, R.
  • Tijs, S.H.

    (Tilburg University, Center for Economic Research)

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    Abstract

    This paper defines models of cooperation among players partition- ing 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 cooper- ating 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 di- vision.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-101.

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    Date of creation: 2008
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    Handle: RePEc:dgr:kubcen:2008101

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    Web page: http://center.uvt.nl

    Related research

    Keywords: fair division; cooperative games; maximin partition;

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    References

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    1. Legut Jerzy & Potters Jos A. M. & Tijs Stef H., 1995. "A Transfer Property of Equilibrium Payoffs in Economies with Land," Games and Economic Behavior, Elsevier, vol. 10(2), pages 355-367, August.
    2. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1995. "A transfer property of equilibrium payoffs in economies with land," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86377, Tilburg University.
    3. Berliant, Marcus, 1985. "Equilibrium models with land : A criticism and an alternative," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 325-340, June.
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    5. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March.
    6. Berliant, M.C. & Dunz, K., 1991. "A Foundation of Location Theory : Exstence of Equilibrium, the Welfare Theorems and Core," RCER Working Papers 298, University of Rochester - Center for Economic Research (RCER).
    7. I. D. Hill, 2008. "Mathematics and Democracy: Designing Better Voting and Fair-division Procedures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 1032-1033.
    8. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    9. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1994. "Economies with land: A game theoretical approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154193, Tilburg University.
    10. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
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