A Strongly Polynomial Algorithm for Linear Exchange Markets

• 成果类型: Article
• 署名作者: Garg, Jugal; Vegh, Laszlo A.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of London; London School Economics & Political Science
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2258
• 发表日期: 2023
• 页码: 487-505
• 关键词: market equilibria; linear exchange markets; strongly polynomial algorithm; two-variable-per-inequality systems

摘要

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 DMalgorithm 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.