IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v172y2017i2d10.1007_s10957-016-0975-1.html
   My bibliography  Save this article

Distributed Price Adjustment Based on Convex Analysis

Author

Listed:
  • Yurii Nesterov

    (Catholic University of Louvain (UCL))

  • Vladimir Shikhman

    (Catholic University of Louvain (UCL))

Abstract

In this paper, we suggest a distributed process of price adjustment toward a partial market equilibrium. As the main contribution, our algorithm of price adjustment is computationally efficient and decentralized. Its convergence properties are crucially based on convex analysis. The proposed price adjustment corresponds to a subgradient scheme for minimizing a special nonsmooth convex function. This function is the total excessive revenue of the market’s participants and its minimizers are equilibrium prices. As the main result, the algorithm of price adjustment is shown to converge to equilibrium prices. Additionally, the market clears on average during the price adjustment process, i.e., by historical averages of supply and demand. Moreover, a global rate of convergence is obtained. We endow our algorithm with decentralized prices by introducing the trade design with price initiative of producers. The latter suggests that producers settle and update their individual prices, and consumers buy at the lowest purchase price.

Suggested Citation

  • Yurii Nesterov & Vladimir Shikhman, 2017. "Distributed Price Adjustment Based on Convex Analysis," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 594-622, February.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-0975-1
    DOI: 10.1007/s10957-016-0975-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0975-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-016-0975-1?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. Ariel Rubinstein, 2012. "Lecture Notes in Microeconomic Theory: The Economic Agent Second Edition," Economics Books, Princeton University Press, edition 2, number 9742.
    3. Franklin M. Fisher, 1972. "On Price Adjustment without an Auctioneer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(1), pages 1-15.
    4. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    5. NESTEROV, Yurii & SHIKHMAN, Vladimir, 2015. "Quasi-monotone subgradient methods for nonsmooth convex minimization," LIDAM Reprints CORE 2670, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Michele Piccione & Ariel Rubinstein, 2007. "Equilibrium in the Jungle," Economic Journal, Royal Economic Society, vol. 117(522), pages 883-896, July.
    7. Yu. Nesterov & V. Shikhman, 2015. "Quasi-monotone Subgradient Methods for Nonsmooth Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 917-940, June.
    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. David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.
    2. Sjur Didrik Flåm, 2019. "Blocks of coordinates, stochastic programming, and markets," Computational Management Science, Springer, vol. 16(1), pages 3-16, February.

    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. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, December.
    2. Alessandro SACCAL, 2020. "The Political Economy Theorem," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 11(2), pages 111-116.
    3. Markus K. Brunnermeier & Alp Simsek & Wei Xiong, 2014. "A Welfare Criterion For Models With Distorted Beliefs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1753-1797.
    4. Yurii Nesterov, 2024. "Primal Subgradient Methods with Predefined Step Sizes," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2083-2115, December.
    5. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    6. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    7. Lasso de la Vega, Casilda & Volij, Oscar & Weinschelbaum, Federico, 2021. "Theft in equilibrium," European Economic Review, Elsevier, vol. 139(C).
    8. Gorno, Leandro, 2019. "Revealed preference and identification," Journal of Economic Theory, Elsevier, vol. 183(C), pages 698-739.
    9. Igor Konnov, 2020. "A Non-monotone Conjugate Subgradient Type Method for Minimization of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 534-546, February.
    10. 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.
    11. Schlee, Edward E. & Ali Khan, M., 2023. "Money-metrics in local welfare analysis: Pareto improvements and equity considerations," Journal of Economic Theory, Elsevier, vol. 213(C).
    12. Schaefer, Alexander, 2021. "Rationality, uncertainty, and unanimity: an epistemic critique of contractarianism," Economics and Philosophy, Cambridge University Press, vol. 37(1), pages 82-117, March.
    13. Akihiko Matsui & Megumi Murakami, 2017. "Demographics, Immigration, and Market Size," CIRJE F-Series CIRJE-F-1060, CIRJE, Faculty of Economics, University of Tokyo.
    14. NESTEROV, Yurii & SHIKHMAN, Vladimir, 2015. "Algorithm of price adjustment for market equilibrium," LIDAM Discussion Papers CORE 2015001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Wright, Austin L. & Sonin, Konstantin & Driscoll, Jesse & Wilson, Jarnickae, 2020. "Poverty and economic dislocation reduce compliance with COVID-19 shelter-in-place protocols," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 544-554.
    16. Janvier D. Nkurunziza, 2005. "Reputation and Credit without Collateral in Africa`s Formal Banking," Economics Series Working Papers WPS/2005-02, University of Oxford, Department of Economics.
    17. Vadim Borokhov, 2014. "On the properties of nodal price response matrix in electricity markets," Papers 1404.3678, arXiv.org, revised Jan 2015.
    18. Gan, Li & Ju, Gaosheng & Zhu, Xi, 2015. "Nonparametric estimation of structural labor supply and exact welfare change under nonconvex piecewise-linear budget sets," Journal of Econometrics, Elsevier, vol. 188(2), pages 526-544.
    19. Peterson, Jeffrey M. & Boisvert, Richard N. & de Gorter, Harry, 1999. "Multifunctionality and Optimal Environmental Policies for Agriculture in an Open Economy," Working Papers 127701, Cornell University, Department of Applied Economics and Management.
    20. Aldasoro, Iñaki & Delli Gatti, Domenico & Faia, Ester, 2017. "Bank networks: Contagion, systemic risk and prudential policy," Journal of Economic Behavior & Organization, Elsevier, vol. 142(C), pages 164-188.

    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:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-0975-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.