Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands
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.
Keywords
Cite
@article{arxiv.1908.07948,
title = {Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands},
author = {Jugal Garg and Edin Husić and László A. Végh},
journal= {arXiv preprint arXiv:1908.07948},
year = {2022}
}
Comments
42 pages, 1 figure. A preliminary version appeared in STACS 2021