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Algorithm of price adjustment for market equilibrium

Author

Listed:
  • NESTEROV, Yurii

    (Universitécatholique de Louvain, CORE, Belgium)

  • SHIKHMAN, Vladimir

    (Université catholique de Louvain, CORE, Belgium)

Abstract
In this paper, we suggest an algorithm for price adjustment towards a partial market equilibrium. Its convergence properties are crucially based on Convex Analysis. Our 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 [16, 18], and its minimizers are equilibrium prices. As the main result, the algorithm of price adjustment is shown to converge to equilibrium prices. Additionally, a market equilibrium clears on average during the price adjustment process. This means that the market clears by historical averages of supply and demand. Moreover, an efficient rate of convergence is obtained. Additionally, we endow our algorithm with decentralized prices by introducing the trade design. The latter suggests that producers settle and update their individual prices, and consumers buy at the lowest purchase price. The proposed price adjustment enjoys a natural behavioral interpretation. First, producers forecast their individual prices to be proportional to their excess demands. For the price update, they subsequently apply an average of these price forecasts over time

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2015001
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    References listed on IDEAS

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    1. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    2. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, vol. 43(1), pages 20-54, October.
    3. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    4. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    5. NESTEROV, Yu. & SHIKHMAN, Vladimir, 2013. "Algorithmic models of market equilibrium," LIDAM Discussion Papers CORE 2013066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    7. 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.
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    Cited by:

    1. Mattéo Godin & Jean Hindriks, 2015. "A Review of critical issues on tax design and tax administration in a global economy and developing countries," BeFinD Working Papers 0107, University of Namur, Department of Economics.
    2. Mouchart, M. & Wunsch, G. & Russo, F., 2015. "The issue of control in multivariate systems, A contribution of structural modelling," LIDAM Discussion Papers ISBA 2015019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Jean J. Gabszewicz & Marco A. Marini & Ornella Tarola, 2015. "Alliance Formation in a Vertically Differentiated Market," DIAG Technical Reports 2015-06, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Dufays, A. & Rombouts, V., 2015. "Sparse Change-Point Time Series Models," LIDAM Discussion Papers CORE 2015032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Mouchart, M. & Wunsch, G. & Russo, F., 2015. "The issue of control in multivariate systems A contribution of structural modelling," LIDAM Discussion Papers CORE 2015029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Balandraud, Eric & Queyranne, Maurice & Tardella, Fabio, 2015. "Largest minimally inversion-complete and pair-complete sets of permutations," LIDAM Discussion Papers CORE 2015009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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