IDEAS home Printed from https://ideas.repec.org/p/usi/wpaper/729.html
   My bibliography  Save this paper

On controlling chaos in a discrete tâtonnement process

Author

Listed:
  • Ahmad K. Naimzada
  • Serena Sordi

Abstract

The simple pure exchange model with two individuals and two goods by Day and Pianigiani (1991), extensively analyzed by Day (1994, Ch. 10) and taken up again by Mukherjy (1999), is discussed and extended with the purpose of showing that chaos in a discrete tâtonnement process of this kind can be controlled if the auctioneer uses a smooth, nonlinear formulation of the price evolution process such that the price adjustment is a sigmoid-shaped function of the excess demand, with given upper and lower limits. This formulation o¤ers some advantages over previous speci?cations. In particular, given the speed of adjustment and the excess demand function, we show that, acting on the lower and/or upper limits that constrain price dynamics, the auctioneer can (i) stabilize the dynamics, (ii) reduce the complexity of the attractor and (iii) increase the economic signi?cance of the adjustment process.

Suggested Citation

  • Ahmad K. Naimzada & Serena Sordi, 2016. "On controlling chaos in a discrete tâtonnement process," Department of Economics University of Siena 729, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:729
    as

    Download full text from publisher

    File URL: http://repec.deps.unisi.it/quaderni/729.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jacques Lesourne & André Orléan & Bernard Walliser, 2006. "Evolutionary Microeconomics," Springer Books, Springer, number 978-3-540-28537-3, April.
    2. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July.
    3. Goeree, Jacob K. & Hommes, Cars & Weddepohl, Claus, 1998. "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 395-410, January.
    4. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
    5. H. Uzawa, 1960. "Walras' Tâtonnement in the Theory of Exchange," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(3), pages 182-194.
    6. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, December.
    7. Kaizouji, Taisei, 1994. "Multiple equilibria and chaotic tatonnement: Applications of the Yamaguti-Matano theorem," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 357-362, August.
    8. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical Dynamics and Economics," Working Paper Series 293, Research Institute of Industrial Economics.
    9. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(4), pages 437-445, October.
    10. Morishima,Michio, 1996. "Dynamic Economic Theory," Cambridge Books, Cambridge University Press, number 9780521563246, January.
    11. Anjan Mukherji, 1999. "A simple example of complex dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 741-749.
    12. Weddepohl, Claus, 1995. "A cautious price adjustment mechanism: Chaotic behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 293-300, July.
    13. Bala, Venkatesh & Majumdar, Mukul & Mitra, Tapan, 1998. "A note on controlling a chaotic tatonnement," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 411-420, January.
    14. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
    15. Saari, Donald G., 1991. "Erratic behavior in economic models," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 3-35, July.
    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. Ahmad K. Naimzada & Serena Sordi, 2018. "On controlling chaos in a discrete†time Walrasian tâtonnement process," Metroeconomica, Wiley Blackwell, vol. 69(1), pages 178-194, February.
    2. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    3. Kaizoji, Taisei, 2010. "Multiple equilibria and chaos in a discrete tâtonnement process," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 597-599, December.
    4. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, April.
    5. van der Laan, G. & Talman, A.J.J., 2002. "Dynamic Adjustment of Supply Constrained Disequilibria to Walrasian Equilibrium," Other publications TiSEM 8c5d443d-92c8-4e82-bcef-3, Tilburg University, School of Economics and Management.
    6. Goeree, Jacob K. & Hommes, Cars & Weddepohl, Claus, 1998. "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 395-410, January.
    7. Kitti, Mitri, 2010. "Convergence of iterative tâtonnement without price normalization," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1077-1091, June.
    8. Anjan Mukherji, 2003. "Competitive Equilibria: Convergence, Cycles or Chaos," ISER Discussion Paper 0591, Institute of Social and Economic Research, Osaka University.
    9. Huang, Weihong, 2001. "Statistical dynamics and Walras' law," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 57-71, September.
    10. Hommes, Cars & Huang, Hai & Wang, Duo, 2005. "A robust rational route to randomness in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1043-1072, June.
    11. Eric Kemp-Benedict, 2011. "Second-Order, Dissipative T\^atonnement: Economic Interpretation and 2-Point Limit Cycles," Papers 1108.0188, arXiv.org, revised Aug 2011.
    12. Richards, Diana & Hays, Jude C., 1998. "Navigating a nonlinear environment: An experimental study of decision making in a chaotic setting," Journal of Economic Behavior & Organization, Elsevier, vol. 35(3), pages 281-308, April.
    13. Tuinstra, Jan, 2000. "A discrete and symmetric price adjustment process on the simplex," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 881-907, June.
    14. Hommes, C.H. & Huang, H. & Wang, D., 2002. "A Robust Rational Route to in a Simple Asset Pricing Model," CeNDEF Working Papers 02-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    15. Herings, Jean-Jacques & van der Laan, Gerard & Talman, Dolf & Venniker, Richard, 1997. "Equilibrium adjustment of disequilibrium prices," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 53-77, February.
    16. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 187-205, June.
    17. Bala, Venkatesh & Majumdar, Mukul & Mitra, Tapan, 1998. "A note on controlling a chaotic tatonnement," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 411-420, January.
    18. Rosser, J. Barkley & Rosser, Marina V, 2023. "A conjoined intellectual journey: Richard H. Day and the journal he founded," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 83-90.
    19. Herings, P.J.J., 1994. "A globally and universally stable quantity adjustment process for an exchange economy with price rigidities," Other publications TiSEM 6f90d995-9065-4ad8-bd04-2, Tilburg University, School of Economics and Management.
    20. Huang, Weihong & Zhang, Yang, 2007. "Distributional dynamics of cautious economic adjustment processes," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 389-407, March.

    More about this item

    Keywords

    Price adjustment; tâtonnement; chaos; control;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:usi:wpaper:729. 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: Fabrizio Becatti (email available below). General contact details of provider: https://edirc.repec.org/data/desieit.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.