Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/222032 
Year of Publication: 
2018
Series/Report no.: 
IEHAS Discussion Papers No. MT-DP - 2018/19
Publisher: 
Hungarian Academy of Sciences, Institute of Economics, Budapest
Abstract: 
An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. In this paper, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our main contribution is threefold. First we present a protocol for integer demands that delivers a proportional solution in fewer queries than all known algorithms. Then we show that our protocol is asymptotically the fastest possible by giving a matching lower bound. Finally, we turn to irrational demands and solve the proportional cake cutting problem by reducing it to the same problem with integer demands only. All results remain valid in a highly general cake cutting model, which can be of independent interest.
Subjects: 
fair division
cake cutting
unequal shares
complexity
JEL: 
C63
C78
Document Type: 
Working Paper

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