Auction algorithms for market equilibrium with weak gross substitute demands and their applications

Garg, Jugal, Husić, Edin ORCID: 0000-0002-6708-5112 and Végh, László A. ORCID: 0000-0003-1152-200X (2021) Auction algorithms for market equilibrium with weak gross substitute demands and their applications. In: Blaser, Markus and Monmege, Benjamin, (eds.) 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021. Leibniz International Proceedings in Informatics, LIPIcs,187. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. ISBN 9783959771801

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Abstract

We consider the Arrow-Debreu exchange market model where agents' demands satisfy the weak gross substitutes (WGS) property. This is a well-studied property, in particular, it gives a sufficient condition for the convergence of the classical tâtonnement dynamics. In this paper, we present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands. Such auction algorithms have been previously known for restricted classes of WGS demands only. As an application of our technique, we obtain an efficient algorithm to find an approximate spendingrestricted market equilibrium for WGS demands, a model that has been recently introduced as a continuous relaxation of the Nash social welfare (NSW) problem. This leads to a polynomial-time constant factor approximation algorithm for NSW with budget separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known for this setting previously.

Item Type:	Book Section
Official URL:	https://drops.dagstuhl.de/opus/portals/lipics/inde...
Additional Information:	© 2021 The Authors; licensed under Creative Commons License CC-BY 4.0.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	21 Jan 2022 11:18
Last Modified:	07 Apr 2024 20:54
URI:	http://eprints.lse.ac.uk/id/eprint/113500

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