Fully Polynomial-Time Approximation Schemes for Fair Rent Division

• 成果类型: Article; Early Access
• 署名作者: Arunachaleswaran, Eshwar Ram; Barman, Siddharth; Rathi, Nidhi
• 署名单位: University of Pennsylvania; Indian Institute of Science (IISC) - Bangalore; Indian Institute of Science (IISC) - Bangalore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1196
• 发表日期: 2021
• 关键词: allocation; complexity; harmony; envy

摘要

We study the problem of fair rent division that entails splitting the rent and allocating the rooms of an apartment among agents in a fair manner (i.e., under the imposed rents, no agent has a strictly stronger preference for any other agent's room). The utility functions specify the cardinal preferences of the agents for the rooms for every possible room rent. Although envy-free solutions are guaranteed to exist under reasonably general utility functions, efficient algorithms for finding them were known only for quasilinear utilities. This work addresses this notable gap and develops a fully polynomial-time approximation scheme for fair rent division with minimal assumptions on the utility functions. Envy-free solutions correspond to equilibria of a two-sided matching market with monetary transfers; hence, this work also provides efficient algorithms for finding approximate equilibria in such markets. We complement the algorithmic results by proving that the fair rent division problem lies in the intersection of the complexity classes polynomial parity arguments on directed graphs and polynomial local search.