A strongly polynomial algorithm for linear exchange markets

Garg, Jugal and Végh, László A. ORCID: 0000-0003-1152-200X (2023) A strongly polynomial algorithm for linear exchange markets. Operations Research, 71 (2). 487 - 505. ISSN 0030-364X

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Abstract

We present a strongly polynomial algorithm for computing an equilibrium in Arrow-Debreu exchange markets with linear utilities. Our algorithm is based on a variant of the weakly polynomial Duan–Mehlhorn (DM) algorithm. We use the DM algorithm as a subroutine to identify revealed edges—that is, pairs of agents and goods that must correspond to the best bang-per-buck transactions in every equilibrium solution. Every time a new revealed edge is found, we use another subroutine that decides if there is an optimal solution using the current set of revealed edges or, if none exists, finds the solution that approximately minimizes the violation of the demand and supply constraints. This task can be reduced to solving a linear program (LP). Even though we are unable to solve this LP in strongly polynomial time, we show that it can be approximated by a simpler LP with two variables per inequality that is solvable in strongly polynomial time.

Item Type:	Article
Official URL:	https://pubsonline.informs.org/journal/opre
Additional Information:	© 2022 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	02 Feb 2022 16:03
Last Modified:	12 Dec 2024 02:50
URI:	http://eprints.lse.ac.uk/id/eprint/113604

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