We initiate the study of multi-layered cake cutting with goal of fairness among a set of agents. We impose a restriction that each agent may only receive a single resource at each time interval. This criterion is reflected in multiple natural settings such as allocating multiple facilities or shift scheduling. We show that under this feasibility constraint envy-free and proportional allocations exist for two resources and at most three agents. We also provide an algorithm for computing proportional allocations for cakes with powers of two layers. This work was done jointly with Dr. Hadi Hosseini of Penn State and Dr. Ayumi Igarashi of the University of Tokyo.
Hosseini, H., Igarashi, A., & Searns, A. (2020, July). Fair Division of Time: Multi-layered Cake Cutting. Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence. Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. https://doi.org/10.24963/ijcai.2020/26