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Geometric division with a fixed point: Not half the cake, but at least 4/9

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  • Andreas Wagener

    (University of Vienna)

Abstract

We study a two-person problem of cutting a homogeneous cake where one player is disadvantaged from the outset: Unlike under the divide-and-choose rule he may only choose a point on the cake through which the other player will then execute a cut and then take the piece that he prefers. We derive the optimal strategy for the disadvantaged player in this game and a lower bound for the share of the cake that he can maximally obtain: It amounts to one third of the cake whenever the cake is bounded. For convex and bounded cakes the minimum share rises to 4/9 of the cake.

Suggested Citation

  • Andreas Wagener, 2006. "Geometric division with a fixed point: Not half the cake, but at least 4/9," Group Decision and Negotiation, Springer, vol. 15(1), pages 43-53, January.
    • Handle: RePEc:spr:grdene:v:15:y:2006:i:1:d:10.1007_s10726-005-9000-z
    DOI: 10.1007/s10726-005-9000-z
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    References listed on IDEAS

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    1. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April.
    2. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
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    Keywords

    cake cutting; unfair division;

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