TY - GEN

T1 - Combinatorial Algorithms for General Linear Arrow-Debreu Markets

AU - Chaudhury, Bhaskar Ray

AU - Mehlhorn, Kurt

N1 - Publisher Copyright:
© Bhaskar Ray Chaudhury and Kurt Mehlhorn.

PY - 2018/12

Y1 - 2018/12

N2 - 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 Õ((n+m)7 log3(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 UΩ(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.

AB - 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 Õ((n+m)7 log3(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 UΩ(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.

KW - Combinatorial algorithms

KW - Equilibrium

KW - Linear exchange markets

UR - http://www.scopus.com/inward/record.url?scp=85079487888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85079487888&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2018.26

DO - 10.4230/LIPIcs.FSTTCS.2018.26

M3 - Conference contribution

AN - SCOPUS:85079487888

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018

A2 - Ganguly, Sumit

A2 - Pandya, Paritosh

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018

Y2 - 11 December 2018 through 13 December 2018

ER -