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Robust Market Equilibria with Uncertain Preferences

Murray, Riley and Kroer, Christian and Peysakhovich, Alex and Shah, Parikshit (2020) Robust Market Equilibria with Uncertain Preferences. In: Thirty-Fourth AAAI Conference on Artificial Intelligence. Vol.34. No.2. Association for the Advancement of Artificial Intelligence (AAAI) , Palo Alto, CA, pp. 2192-2199. ISBN 978-1-57735-835-0.

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The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences, have a budget of real or fake currency, and a set of prices for items and allocations is computed that sets demand equal to supply. An important real world issue with such mechanisms is that individual valuations are often only imperfectly known. In this paper, we show how concepts from classical market equilibrium can be extended to reflect such uncertainty. We show that in linear, divisible Fisher markets a robust market equilibrium (RME) always exists; this also holds in settings where buyers may retain unspent money. We provide theoretical analysis of the allocative properties of RME in terms of envy and regret. Though RME are hard to compute for general uncertainty sets, we consider some natural and tractable uncertainty sets which lead to well behaved formulations of the problem that can be solved via modern convex programming methods. Finally, we show that very mild uncertainty about valuations can cause RME allocations to outperform those which take estimates as having no underlying uncertainty.

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Additional Information:© 2020 Association for the Advancement of Artificial Intelligence. Published 2020-04-03. The majority of this research was conducted while the first and second authors were employed by Facebook, as intern and postdoc, respectively. The first author was supported (in part) by a National Science Foundation Graduate Research Fellowship.
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NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20210910-230235843
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Official Citation:Murray, R., Kroer, C., Peysakhovich, A., & Shah, P. (2020). Robust Market Equilibria with Uncertain Preferences. Proceedings of the AAAI Conference on Artificial Intelligence, 34(02), 2192-2199.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110819
Deposited By: Tony Diaz
Deposited On:13 Sep 2021 17:32
Last Modified:13 Sep 2021 17:32

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