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

Andreas Wagener

Group Decision and Negotiation, 2006, vol. 15, issue 1, No 3, 43-53

Abstract: 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.

Keywords: cake cutting; unfair division (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10726-005-9000-z

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