论文标题
多层蛋糕的公平师
Fair Division of Multi-layered Cakes
论文作者
论文摘要
我们考虑将多层切割蛋糕切割，以便在两种约束的一组代理中分配众多可分割资源（蛋糕层）：连续性和可行性。我们首先在一个名为``一双刀子''的多层蛋糕中引入了一种新的计算模型。然后，我们使用新的计算模型显示了两种代理和两层的确切多分配的存在。我们演示了三层蛋糕的可行且连续的比例多分配的计算程序，用于三个以上的代理。最后，我们开发了一种计算任何数字$ n \ geq 2^a3 $的代理和$ 2^a3 $ layers的技术分配的技术，其中$ a $是任何正整数。
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.
