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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
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    References listed on IDEAS

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    1. Ariel Rubinstein, 2012. "Lecture Notes in Microeconomic Theory: The Economic Agent Second Edition," Economics Books, Princeton University Press, edition 2, number 9742.
    2. 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.
    3. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    4. 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.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. 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).
    7. Michele Piccione & Ariel Rubinstein, 2007. "Equilibrium in the Jungle," Economic Journal, Royal Economic Society, vol. 117(522), pages 883-896, July.
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    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.

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