Almost envy-free allocations with connected bundles

• 成果类型: Article
• 署名作者: Bilo, Vittorio; Caragiannis, Ioannis; Flammini, Michele; Igarashi, Ayumi; Monaco, Gianpiero; Peters, Dominik; Vinci, Cosimo; Zwicker, William S.
• 署名单位: University of Salento; Aarhus University; Gran Sasso Science Institute (GSSI); Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; University of L'Aquila; University of Toronto; Union College
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.11.006
• 发表日期: 2022
• 页码: 197-221
• 关键词: Envy-free division; Cake-cutting; resource allocation; Algorithmic game theory

摘要

We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph. If the graph is a path and the utility functions are monotonic over bundles, we show the existence of EF1 allocations for at most four agents, and the existence of EF2 allocations for any number of agents; our proofs involve discrete analogues of the Stromquist's moving-knife protocol and the Su-Simmons argument based on Sperner's lemma. For identical utilities, we provide a polynomial-time algorithm that computes an EF1 allocation for any number of agents. For the case of two agents, we characterize the class of graphs that guarantee the existence of EF1 allocations as those whose biconnected components are arranged in a path; this property can be checked in linear time. (C) 2021 Elsevier Inc. All rights reserved.