IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1132.html
   My bibliography  Save this paper

Price Variations in a Stock Market with Many Agents

Author

Listed:

Abstract

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between "rational" traders whose behavior is derived from fundamental analysis of the stock, including dividends, and "noise traders," whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, "bubbles" often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is large, the market price is generally locked within the price range they define.

Suggested Citation

  • P. Bak & M. Paczuski & Martin Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Cowles Foundation Discussion Papers 1132, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1132
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1132.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    2. Alain Arneodo & Jean-Philippe Bouchaud & Rama Cont & Jean-Francois Muzy & Marc Potters & Didier Sornette, 1996. "Comment on "Turbulent cascades in foreign exchange markets"," Science & Finance (CFM) working paper archive 9607120, Science & Finance, Capital Fund Management.
    3. Grandmont, Jean-Michel, 1993. "Behavioural heterogeneity and Cournot oligopoly equilibrium," Ricerche Economiche, Elsevier, vol. 47(2), pages 167-187, June.
    Full references (including those not matched with items on IDEAS)

    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. Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
    2. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
    3. Hehenkamp, Burkhard & Kaarbøe, Oddvar M., 2003. "Imitators and Optimizers in a Changing Environment," Working Papers in Economics 03/03, University of Bergen, Department of Economics.
    4. Jean-Michel Grandmont, 2017. "Behavioral Heterogeneity: Pareto Distributions of Homothetic Preference Scales and Aggregate Expenditures Income Elasticities," Discussion Paper Series DP2017-31, Research Institute for Economics & Business Administration, Kobe University.
    5. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 684, University of Warwick, Department of Economics.
    6. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
    7. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    8. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
    9. Steffen Huck & Hans-Theo Normann & Jörg Oechssler, 2002. "Stability of the Cournot process - experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 123-136.
    10. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    11. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    12. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    13. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2006. "Vertical Differentiation And The Distribution Of Income," Bulletin of Economic Research, Wiley Blackwell, vol. 58(4), pages 345-367, October.
    14. Rotundo, G., 2004. "Neural networks for large financial crashes forecast," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 77-80.
    15. Benassi, Corrado & Castellani, Massimiliano & Mussoni, Maurizio, 2016. "Price equilibrium and willingness to pay in a vertically differentiated mixed duopoly," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 86-96.
    16. Peitz, Martin, 2000. "Aggregation in a Model of Price Competition," Journal of Economic Theory, Elsevier, vol. 90(1), pages 1-38, January.
    17. Harrington, Joseph Jr. & Chang, Myong-Hun, 2005. "Co-evolution of firms and consumers and the implications for market dominance," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 245-276, January.
    18. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," Economic Research Papers 269566, University of Warwick - Department of Economics.
    19. Stegeman, Mark & Rhode, Paul, 2004. "Stochastic Darwinian equilibria in small and large populations," Games and Economic Behavior, Elsevier, vol. 49(1), pages 171-214, October.
    20. Ania, Ana B. & Troger, Thomas & Wambach, Achim, 2002. "An evolutionary analysis of insurance markets with adverse selection," Games and Economic Behavior, Elsevier, vol. 40(2), pages 153-184, August.

    More about this item

    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:cwl:cwldpp:1132. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.