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