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arXiv · 2208.00726

Fair Division of Multi-layered Cakes

Mohammad Azharuddin Sanpui
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Abstract

We consider multi-layered cake cutting in order to fairly allocate numerous divisible resources (layers of cake) among a group of agents under two constraints: contiguity and feasibility. We first introduce a new computational model in a multi-layered cake named ``a pair of knives''. Then, we show the existence of an exact multi-allocation for two agents and two layers using the new computational model. We demonstrate the computation procedure of a feasible and contiguous proportional multi-allocation over a three-layered cake for more than three agents. Finally, we develop a technique for computing proportional allocations for any number $n\geq 2^a3$ of agents and $2^a3$ layers, where $a$ is any positive integer.

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Mohammad Azharuddin Sanpui. 2022-08-01. Fair Division of Multi-layered Cakes. https://arxiv.org/abs/2208.00726

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