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Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications

Authors Jugal Garg , Edin Husić , László A. Végh

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Author Details

Jugal Garg
  • University of Illinois at Urbana-Champaign, IL, USA
Edin Husić
  • Department of Mathematics, The London School of Economics and Political Science, UK
László A. Végh
  • Department of Mathematics, The London School of Economics and Political Science, UK

Funding

Jugal Garg was supported by the NSF CAREER Award 1942321. Edin Husić and László A. Végh were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement ScaleOpt–757481).

Acknowledgements

We would like to thank anonymous referees for their comments and suggestions that have helped to improve the presentation of the paper.

Cite AsGet BibTex

Jugal Garg, Edin Husić, and László A. Végh. Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.33

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 spending-restricted 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • auction algorithm
  • weak gross substitutes
  • Fisher equilibrium
  • Gale equilibrium
  • Nash social welfare

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