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Proportional Fair Division of Multi-layered Cakes | | Mohammad Azharuddin Sanpui
; | | Date: |
1 Aug 2022 | | Abstract: | We study the multi-layered cake cutting problem, where the multi-layered cake
is divided among agents proportionally. This problem was initiated by Hosseini
et al.(2020) under two constraints, one is contiguity and the other is
feasibility. Basically we will show the existence of proportional
multi-allocation for any number of agents with any number of preferences that
satisfies contiguity and feasibility constraints using the idea of switching
point for individual agent and majority agents. First we show that exact
feasible multi-allocation is guaranteed to exist for two agents with two types
of preferences. Second we see that we always get an envy-free multi-allocation
that satisfies the feasibility and contiguity constraints for three agent with
two types of preferences such that each agent has a share to each layer even
without the knowledge of the unique preference of the third agent. | | Source: | arXiv, 2208.00726 | | Services: | Forum | Review | PDF | Favorites | |
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