Fair Division of Multi-layered Cakes
This addresses fair division in multi-resource scenarios for applications like resource allocation, but it is incremental as it builds on existing cake-cutting theory.
The paper tackles the problem of fairly allocating multiple divisible resources (layered cakes) among agents under contiguity and feasibility constraints, introducing a 'pair of knives' computational model and proving existence for two agents and two layers, with computational procedures for more agents and layers.
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.