On the Fair Division of a Random Object

• 成果类型: Article
• 署名作者: Bogomolnaia, Anna; Moulin, Herve; Sandomirskiy, Fedor
• 署名单位: University of Glasgow; HSE University (National Research University Higher School of Economics); Technion Israel Institute of Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2021.3973
• 发表日期: 2022
• 页码: 1174-1194
• 关键词: fair division; goods or bads; prior-independent mechanisms; competitive ratio

摘要

Ann likes oranges much more than apples; Bob likes apples much more than oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability. Giving one half to each agent is fair for each realization of the fruit. However, agreeing that whatever fruit appears will go to the agent who likes it more gives a higher expected utility to each agent and is fair in the average sense: in expectation, each agent prefers the allocation to the equal division of the fruit; that is, the agent gets a fair share. We turn this familiar observation into an economic design problem: upon drawing a random object (the fruit), we learn the realized utility of each agent and can compare it to the mean of the agent's distribution of utilities; no other statistical information about the distribution is available. We fully characterize the division rules using only this sparse information in the most efficient possible way while giving everyone a fair share. Although the probability distribution of individual utilities is arbitrary and mostly unknown to the manager, these rules perform in the same range as the best rule when the manager has full access to this distribution.