论文标题
公平的时间：多层蛋糕切割
Fair Division of Time: Multi-layered Cake Cutting
论文作者
论文摘要
我们启动对多层蛋糕切割的研究，目的是在一组代理商中相当分配多个可分配的资源（蛋糕层）。关键要求是，每个代理只能在每个时间间隔中使用一个资源。几种现实生活中的应用显示出对重叠作品的限制。例如，分配多个设施和资源的时间间隔或将转移分配给医疗专业人员。我们研究了无嫉妒和比例分配的存在和计算。我们表明，当层数为两个时，可以保证有多达三种具有两种偏好类型的代理的嫉妒分配，最多可为三种具有两种偏好的代理存在。我们还表明，每个代理在轻度条件下，在代理的偏好中，每个代理都会在任何数量的代理和层中都有多项式界限的间隔数量。我们进一步设计了一种用于计算任何数量代理和层的计算比例分配的算法。
We initiate the study of multi-layered cake cutting with the goal of fairly allocating multiple divisible resources (layers of a cake) among a set of agents. The key requirement is that each agent can only utilize a single resource at each time interval. Several real-life applications exhibit such restrictions on overlapping pieces; for example, assigning time intervals over multiple facilities and resources or assigning shifts to medical professionals. We investigate the existence and computation of envy-free and proportional allocations. We show that envy-free allocations that are both feasible and contiguous are guaranteed to exist for up to three agents with two types of preferences, when the number of layers is two. We also show that envy-free feasible allocations where each agent receives a polynomially bounded number of intervals exist for any number of agents and layers under mild conditions on agents' preferences. We further devise an algorithm for computing proportional allocations for any number of agents and layers.
