On the Fair Division of a Random Object

Anna Bogomolnaia (), Herve Moulin and Fedor Sandomirskiy ()
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Anna Bogomolnaia: Adam Smith Business School, University of Glasgow, Glasgow G12 8QQ, United Kingdom; International Laboratory of Game Theory and Decision Making, Higher School of Economics, St. Petersburg 194100, Russia
Fedor Sandomirskiy: International Laboratory of Game Theory and Decision Making, Higher School of Economics, St. Petersburg 194100, Russia; The Faculty of Industrial Engineering and Management, Technion, Haifa 3200003, Israel

Management Science, 2022, vol. 68, issue 2, 1174-1194

Abstract: 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.

Keywords: fair division; goods or bads; prior-independent mechanisms; competitive ratio (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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http://dx.doi.org/10.1287/mnsc.2021.3973 (application/pdf)

Related works:
Working Paper: On the fair division of a random object (2021)
Working Paper: On the Fair Division of a Random Object (2021)
Working Paper: On the Fair Division of a Random Object (2021)
Working Paper: On the fair division of a random object (2020)
Working Paper: On the fair division of a random object (2020)
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