IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v60y2012i5p1245-1248.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1120.1113
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1120.1113?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zekhov, M. & Pilnik, N. & Radionov, S., 2025. "Constructing a set of equilibrium prices in a generalized distributed markets model," Journal of the New Economic Association, New Economic Association, vol. 67(2), pages 25-44.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yun Kuen Cheung & Richard Cole & Yixin Tao, 2025. "Proportional Response Dynamics in Gross Substitutes Markets," Papers 2506.02852, arXiv.org.
    2. Nikhil Garg & Ashish Goel & Benjamin Plaut, 2021. "Markets for public decision-making," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 755-801, May.
    3. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    4. Sandomirskiy, Fedor & Ushchev, Philip, 2024. "The geometry of consumer preference aggregation," CEPR Discussion Papers 19100, C.E.P.R. Discussion Papers.
    5. Denizalp Goktas & Jiayi Zhao & Amy Greenwald, 2023. "T\^atonnement in Homothetic Fisher Markets," Papers 2306.04890, arXiv.org, revised Feb 2025.
    6. Gabriel P. Andrade & Rafael Frongillo & Elliot Gorokhovsky & Sharadha Srinivasan, 2021. "Graphical Economies with Resale," Papers 2106.14397, arXiv.org.
    7. Jalota, Devansh & Pavone, Marco & Qi, Qi & Ye, Yinyu, 2023. "Fisher markets with linear constraints: Equilibrium properties and efficient distributed algorithms," Games and Economic Behavior, Elsevier, vol. 141(C), pages 223-260.
    8. Jean-Sébastien Lenfant & Jérôme Lallement, 2004. "L'équilibre général comme savoir : de Walras à nos jours," Working Papers hal-01765036, HAL.
    9. Denizalp Goktas & Enrique Areyan Viqueira & Amy Greenwald, 2021. "A Consumer-Theoretic Characterization of Fisher Market Equilibria," Papers 2107.08153, arXiv.org, revised Jan 2022.
    10. Kamesh Munagala & Yiheng Shen & Kangning Wang & Zhiyi Wang, 2021. "Approximate Core for Committee Selection via Multilinear Extension and Market Clearing," Papers 2110.12499, arXiv.org.
    11. K. Vela Velupillai, 2011. "The Phillips Machine, the Analogue Computing Tradition in Economics and Computability," Economia politica, Società editrice il Mulino, issue 1, pages 39-62.
    12. Bongers, Anelí & Molinari, Benedetto & Torres, José L., 2022. "Computers, Programming and Dynamic General Equilibrium Macroeconomic Modeling," MPRA Paper 112505, University Library of Munich, Germany.
    13. Chuangyin Dang & Yinyu Ye & Zhisu Zhu, 2011. "An interior-point path-following algorithm for computing a Leontief economy equilibrium," Computational Optimization and Applications, Springer, vol. 50(2), pages 223-236, October.
    14. 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.
    15. Denizalp Goktas & Amy Greenwald, 2022. "Gradient Descent Ascent in Min-Max Stackelberg Games," Papers 2208.09690, arXiv.org.
    16. Allan Borodin & Akash Rakheja, 2019. "Electronic markets with multiple submodular buyers," Papers 1907.11915, arXiv.org, revised Sep 2019.
    17. Moshe Babaioff & Noam Nisan & Inbal Talgam-Cohen, 2021. "Competitive Equilibrium with Indivisible Goods and Generic Budgets," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 382-403, February.
    18. K. Vela Velupillai & Stefano Zambelli, 2010. "Computation in Economics," ASSRU Discussion Papers 1001, ASSRU - Algorithmic Social Science Research Unit.
    19. Cheung, Yun Kuen & Cole, Richard & Devanur, Nikhil R., 2020. "Tatonnement beyond gross substitutes? Gradient descent to the rescue," Games and Economic Behavior, Elsevier, vol. 123(C), pages 295-326.
    20. Simina Br^anzei & Fedor Sandomirskiy, 2019. "Algorithms for Competitive Division of Chores," Papers 1907.01766, arXiv.org, revised Jul 2023.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1245-1248. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.