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Computer Science > Computer Science and Game Theory

arXiv:1908.07948 (cs)
[Submitted on 21 Aug 2019 (v1), last revised 1 May 2022 (this version, v4)]

Title:Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands

Authors:Jugal Garg, Edin Husić, László A. Végh
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Abstract:We consider the Arrow--Debreu exchange market model under the assumption that the agents' demands satisfy the weak gross substitutes (WGS) property. We present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands assuming the availability of a price update oracle. We exhibit specific implementations of such an oracle for WGS demands with bounded price elasticities and for Gale demand systems.
As an application of our result, 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 the NSW problem with capped additive separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known for this setting previously.
Comments: 42 pages, 1 figure. A preliminary version appeared in STACS 2021
Subjects: Computer Science and Game Theory (cs.GT)
Cite as: arXiv:1908.07948 [cs.GT]
  (or arXiv:1908.07948v4 [cs.GT] for this version)
  https://doi.org/10.48550/arXiv.1908.07948

Submission history

From: Edin Husic [view email]
[v1] Wed, 21 Aug 2019 15:57:12 UTC (49 KB)
[v2] Thu, 13 Feb 2020 13:38:06 UTC (51 KB)
[v3] Wed, 5 Aug 2020 12:13:18 UTC (625 KB)
[v4] Sun, 1 May 2022 15:32:37 UTC (1,289 KB)
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