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On the Fair Division of a Random Object

Anna Bogomolnaia (), Herve Moulin () and Fedor Sandomirskiy
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Anna Bogomolnaia: HSE St Petersburg - Higher School of Economics - St Petersburg, University of Glasgow, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Fedor Sandomirskiy: HSE St Petersburg - Higher School of Economics - St Petersburg

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis.

Date: 2021-03-23
New Economics Papers: this item is included in nep-des and nep-upt
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-03507995
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Published in Management Science, INFORMS, 2021, 21 p. ⟨10.1287/mnsc.2021.3973⟩

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Related works:
Working Paper: On the fair division of a random object (2021) Downloads
Working Paper: On the Fair Division of a Random Object (2021) Downloads
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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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-03507995

DOI: 10.1287/mnsc.2021.3973

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