Combinatorial Algorithms for General Linear Arrow-Debreu Markets

Authors Bhaskar Ray Chaudhury, Kurt Mehlhorn

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Bhaskar Ray Chaudhury
  • MPI for Informatics, Saarland Informatics Campus, Graduate School of Computer Science Saarbrücken, Germany
Kurt Mehlhorn
  • MPI for Informatics, Saarland Informatics Campus, Saarbrücken, Germany

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Bhaskar Ray Chaudhury and Kurt Mehlhorn. Combinatorial Algorithms for General Linear Arrow-Debreu Markets. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We present a combinatorial algorithm for determining the market clearing prices of a general linear Arrow-Debreu market, where every agent can own multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu markets consider the case where each agent can own all of one good only. We present an O~((n+m)^7 log^3(UW)) algorithm where n, m, U and W refer to the number of agents, the number of goods, the maximal integral utility and the maximum quantity of any good in the market respectively. The algorithm refines the iterative algorithm of Duan, Garg and Mehlhorn using several new ideas. We also identify the hard instances for existing combinatorial algorithms for linear Arrow-Debreu markets. In particular we find instances where the ratio of the maximum to the minimum equilibrium price of a good is U^{Omega(n)} and the number of iterations required by the existing iterative combinatorial algorithms of Duan, and Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the two algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
  • Linear Exchange Markets
  • Equilibrium
  • Combinatorial Algorithms


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