IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpco/9508001.html
   My bibliography  Save this paper

The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes

Author

Listed:
  • John Q. Cheng

    (University of Michigan)

  • Michael P. Wellman

    (University of Michigan)

Abstract

The WALRAS algorithm calculates competitive equilibria via a distributed tatonnement-like process, in which agents submit single-good demand functions to market-clearing auctions. The algorithm is asynchronous and decentralized with respect to both agents and markets, making it suitable for distributed implementation. We present a formal description of this algorithm, and prove that it converges under the standard assumption of gross substitutability. We relate our results to the literature on general equilibrium stability and some more recent work on decentralized algorithms. We present some experimental results as well, particularly for cases where the assumptions required to guarantee convergence do not hold. Finally, we consider some extensions and generalizations to the WALRAS algorithm.

Suggested Citation

  • John Q. Cheng & Michael P. Wellman, 1995. "The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes," Computational Economics 9508001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpco:9508001
    Note: Type of Document - postscript; pages: 23 ; figures: included. Submitted for publication
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/comp/papers/9508/9508001.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/comp/papers/9508/9508001.ps.gz
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    2. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550.
    3. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-999, September.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693, Elsevier.
    5. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    6. Campbell,Donald E., 1987. "Resource Allocation Mechanisms," Cambridge Books, Cambridge University Press, number 9780521319904.
    7. Reiter, Stanley & Simon, Carl P., 1992. "Decentralized dynamic processes for finding equilibrium," Journal of Economic Theory, Elsevier, vol. 56(2), pages 400-425, April.
    8. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    9. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    10. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    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. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
    2. Nielsen, Kurt, 2005. "Auctioning Payment Entitlements," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24566, European Association of Agricultural Economists.
    3. William E. Walsh & Michael P. Wellman, 1999. "Efficiency and Equilibrium in Task Allocation Economics with Hierarchical Dependencies," Working Papers 99-07-049, Santa Fe Institute.
    4. Bill Gibson, 2007. "A Multi-Agent Systems Approach to Microeconomic Foundations of Macro," UMASS Amherst Economics Working Papers 2007-10, University of Massachusetts Amherst, Department of Economics.
    5. Javad Khazaei & Anthony Downward & Golbon Zakeri, 2014. "Modelling counter-intuitive effects on cost and air pollution from intermittent generation," Annals of Operations Research, Springer, vol. 222(1), pages 389-418, November.
    6. Rajiv T. Maheswaran & Tamer Başar, 2003. "Nash Equilibrium and Decentralized Negotiation in Auctioning Divisible Resources," Group Decision and Negotiation, Springer, vol. 12(5), pages 361-395, September.
    7. Wurman, Peter R. & Wellman, Michael P. & Walsh, William E., 2001. "A Parametrization of the Auction Design Space," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 304-338, April.
    8. Eymann, Torsten & Streitberger, Werner & Reinicke, Michael & Freitag, Felix & Chacin, Pablo & Chao, Isaac & Schnizler, Björn & Veit, Daniel, 2007. "Preliminary specification and design documentation for software components to achieve catallaxy in computational systems," Bayreuth Reports on Information Systems Management 2, University of Bayreuth, Chair of Information Systems Management.
    9. Kurt Nielsen & Jesper Troelsgaard Nielsen, 2010. "An Allocatively Efficient Auction Market for Payment Entitlements?," MSAP Working Paper Series 03_2010, University of Copenhagen, Department of Food and Resource Economics.
    10. Dennis J. Zhang & Itai Gurvich & Jan A. Van Mieghem & Eric Park & Robert S. Young & Mark V. Williams, 2016. "Hospital Readmissions Reduction Program: An Economic and Operational Analysis," Management Science, INFORMS, vol. 62(11), pages 3351-3371, November.
    11. Sandholm, Tuomas W. & Lesser, Victor R., 2001. "Leveled Commitment Contracts and Strategic Breach," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 212-270, April.

    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. Lilia Maliar & Serguei Maliar, 2005. "An Analytical Construction Of Constantinides¿ Social Utility Function," Working Papers. Serie AD 2005-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Sabiou M. Inoua & Vernon L. Smith, 2020. "The Classical Theory of Supply and Demand," Working Papers 20-11, Chapman University, Economic Science Institute.
    3. Vernon L. Smith & Sabiou M. Inoua, 2019. "Classical Economics: Lost and Found," Working Papers 19-15, Chapman University, Economic Science Institute.
    4. Michael Jerison, 2023. "Social welfare and the unrepresentative representative consumer," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(1), pages 5-28, February.
    5. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    6. Mervyn Allister King, 1993. "Debt Deflation: Theory and Evidence," FMG Discussion Papers dp175, Financial Markets Group.
    7. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    8. David F Hendry & John N J Muellbauer, 2018. "The future of macroeconomics: macro theory and models at the Bank of England," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 34(1-2), pages 287-328.
    9. Grandmont, Jean-Michel, 1992. "Transformations of the commodity space, behavioral heterogeneity, and the aggregation problem," Journal of Economic Theory, Elsevier, vol. 57(1), pages 1-35.
    10. Choudhary, M. Ali & Michael Orszag, J., 2008. "A cobweb model with local externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 821-847, March.
    11. Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2011. "Aggregation without the aggravation? Nonparametric analysis of the representative consumer," Working Papers of Department of Economics, Leuven ces11.36, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    12. Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2013. "Gorman revisited: nonparametric conditions for exact linear aggregation," Working Papers of Department of Economics, Leuven ces13.05, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    13. Hardle, Wolfgang & Kirman, Alan, 1995. "Nonclassical demand : A model-free examination of price-quantity relations in the Marseille fish market," Journal of Econometrics, Elsevier, vol. 67(1), pages 227-257, May.
    14. King, Mervyn, 1993. "Debt inflation: theory and evidence," LSE Research Online Documents on Economics 119181, London School of Economics and Political Science, LSE Library.
    15. Pierre-André Chiappori & Ivar Ekeland & Felix Kübler & Heracles M. Polemarchakis, 1999. "The Identification of Preferences from Equilibrium Prices," Working Papers hal-00598229, HAL.
    16. Barnett, William A. & Serletis, Apostolos, 2008. "Measuring Consumer Preferences and Estimating Demand Systems," MPRA Paper 12318, University Library of Munich, Germany.
    17. Pierre-André Chiappori, 1990. "La théorie du consommateur est-elle réfutable ?," Revue Économique, Programme National Persée, vol. 41(6), pages 1001-1026.
    18. Markus C. Becker & Thorbjørn Knudsen, 2017. "Heterogeneity of habits as a foundation for Schumpeterian economic policy," Journal of Evolutionary Economics, Springer, vol. 27(1), pages 43-62, January.
    19. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
    20. Masao Ogaki, 2003. "Aggregation under Complete Markets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 977-986, October.

    More about this item

    Keywords

    tatonnement; distributed computation; progressive equilibration;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    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:wpa:wuwpco:9508001. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.