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On the fair division of a random object

Bogomolnaia, A. , Moulin, H. and Sandomirskiy, F. (2022) On the fair division of a random object. Management Science, 68(2), pp. 1174-1194. (doi: 10.1287/mnsc.2021.3973)

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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 his allocation to the equal division of the fruit, i.e., he 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 his 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bogomolnaia, Professor Anna and Moulin, Professor Herve
Authors: Bogomolnaia, A., Moulin, H., and Sandomirskiy, F.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Management Science
Publisher:INFORMS
ISSN:0025-1909
ISSN (Online):1526-5501
Published Online:23 March 2021
Copyright Holders:Copyright © 2021 INFORMS
First Published:First published in Management Science 68(2): 1174-1194
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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