A strongly polynomial algorithm for linear exchange markets

Garg, Jugal and Végh, László A. ORCID: 0000-0003-1152-200X (2019) A strongly polynomial algorithm for linear exchange markets. In: Charikar, Moses and Cohen, Edith, (eds.) STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing. UNSPECIFIED, pp. 54-65. ISBN 9781450367059

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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, i.e. pairs of agents and goods that must correspond to 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:	Book Section
Additional Information:	© 2019 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics H Social Sciences > HB Economic Theory
Date Deposited:	19 Jun 2019 15:30
Last Modified:	13 Sep 2024 23:34
URI:	http://eprints.lse.ac.uk/id/eprint/101048

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