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A Simple Approximation Algorithm for Computing Arrow-Debreu Prices

Author

Listed:
  • Mehdi Ghiyasvand

    (Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran)

  • James B. Orlin

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider the Arrow-Debreu market with linear utilities in which there is a set G of divisible goods and a set B of buyers. Each buyer starts with an initial endowment of goods. The buyer's utility function is a linearly separable function of the goods that the buyer purchases. We develop a simple and efficient algorithm for determining an approximate market equilibrium. Our algorithm finds an (epsilon)-approximate solution in O ( n /(epsilon)(| B || G |)) time, where n = | B | + | G |. The running time can be further improved to O ( n /(epsilon)( m + | B |log| B |)) where m is the number of pairs ( i, j ) such that buyer i has some utility for purchasing good j .

Suggested Citation

  • Mehdi Ghiyasvand & James B. Orlin, 2012. "A Simple Approximation Algorithm for Computing Arrow-Debreu Prices," Operations Research, INFORMS, vol. 60(5), pages 1245-1248, October.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1245-1248
    DOI: 10.1287/opre.1120.1113
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    References listed on IDEAS

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    1. William C. Brainard & Herbert E. Scarf, 2005. "How to Compute Equilibrium Prices in 1891," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January.
    2. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
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    Cited by:

    1. Jun Tong & Jian-Qiang Hu & Jianxin You, 2019. "Asynchronous Algorithms for Computing Equilibrium Prices in a Capital Asset Pricing Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-17, October.
    2. Tong, Jun & Hu, Jiaqiao & Hu, Jianqiang, 2017. "Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints," European Journal of Operational Research, Elsevier, vol. 256(1), pages 24-34.

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