Fair Division of Multi-layered Cakes
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909138569658368 |
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| author | Sanpui, Mohammad Azharuddin |
| author_facet | Sanpui, Mohammad Azharuddin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00726 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fair Division of Multi-layered Cakes Sanpui, Mohammad Azharuddin Artificial Intelligence Computer Science and Game Theory 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. |
| title | Fair Division of Multi-layered Cakes |
| topic | Artificial Intelligence Computer Science and Game Theory |
| url | https://arxiv.org/abs/2208.00726 |