IDEAS home Printed from https://ideas.repec.org/a/spr/joevec/v2y1992i3p233-65.html
   My bibliography  Save this article

The Master Equation Approach to Nonlinear Economics

Author

Listed:
  • Weidlich, Wolfgang
  • Braun, Martin

Abstract

A concept for modelling nonlinear economic dynamics is presented and exemplified by a concrete model. Generally, a configuration of macroeconomic variables is considered whose probabilistic evolution is coupled to the decision-making of agents and is described by a master equation. The transition rates in the master equation are modelled in terms of utility measures of the agents. Non-linear dynamic meanvalue equations can be derived from the master equation. The concrete model describes firms producing substitutable durable commodities. They compete with respect to the quality of their products, and a positive feedback between quality enhancement and customer's reaction to quality is assumed. The case of two competing firms is treated explicitly. It is shown that beyond a critical value of a "competitivity parameter" a homogenous market will develop into an inhomogenous one with a winner and a loser firm.

Suggested Citation

  • Weidlich, Wolfgang & Braun, Martin, 1992. "The Master Equation Approach to Nonlinear Economics," Journal of Evolutionary Economics, Springer, vol. 2(3), pages 233-265, October.
    • Handle: RePEc:spr:joevec:v:2:y:1992:i:3:p:233-65
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Verspagen, Bart, 1998. "Special issue on the evolutionary analysis of innovation," Structural Change and Economic Dynamics, Elsevier, vol. 9(1), pages 1-3, March.
    2. Helbing, Dirk & Kern, Daniel, 2000. "Non-equilibrium price theories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 259-268.
    3. Ilaria Foroni & Anna Agliari, 2008. "Complex Price Dynamics in a Financial Market with Imitation," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 21-36, September.
    4. Salarieh, Hassan & Alasty, Aria, 2008. "Delayed feedback control via minimum entropy strategy in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 851-860.
    5. J. Barkley Rosser, 1999. "On the Complexities of Complex Economic Dynamics," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 169-192, Fall.
    6. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    7. Simone Landini & Mauro Gallegati, 2014. "Heterogeneity, interaction and emergence: effects of composition," International Journal of Computational Economics and Econometrics, Inderscience Enterprises Ltd, vol. 4(3/4), pages 339-361.
    8. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.
    9. Cantner, Uwe & Pyka, Andreas, 1998. "Technological evolution -- an analysis within the knowledge-based approach," Structural Change and Economic Dynamics, Elsevier, vol. 9(1), pages 85-107, March.
    10. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
    11. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
    12. Silverberg, Gerald, 1997. "Evolutionary modeling in economics : recent history and immediate prospects," Research Memorandum 008, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    13. Yu, Wenhua & Yang, Kun & Wei, Yu & Lei, Likun, 2018. "Measuring Value-at-Risk and Expected Shortfall of crude oil portfolio using extreme value theory and vine copula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1423-1433.
    14. Karolina Safarzyńska & Jeroen Bergh, 2010. "Evolutionary models in economics: a survey of methods and building blocks," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 329-373, June.
    15. Simone Landini & Mauro Gallegati & Joseph Stiglitz, 2015. "Economies with heterogeneous interacting learning agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 91-118, April.
    16. Hawkins, Raymond J., 2011. "Lending sociodynamics and economic instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4355-4369.
    17. Carrillo Murillo, David Guillermo & Liedtke, Gernot, 2013. "A model for the formation of colloidal structures in freight transportation: The case of hinterland terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 55-70.
    18. Schoder, Detlef, 2000. "Forecasting the success of telecommunication services in the presence of network effects," Information Economics and Policy, Elsevier, vol. 12(2), pages 181-200, June.
    19. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
    20. Sinha, Amit & Horvath, Philip A. & Beason, Tyler & Roos, Kelly R., 2019. "Simulation of a financial market: The possibility of catastrophic disequilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 13-16.
    21. Wang, Lu & Ma, Feng & Hao, Jianyang & Gao, Xinxin, 2021. "Forecasting crude oil volatility with geopolitical risk: Do time-varying switching probabilities play a role?," International Review of Financial Analysis, Elsevier, vol. 76(C).
    22. Woeckener, Bernd W., 1998. "The competition of user networks: Ergodicity, lock-ins, and metastability," Tübinger Diskussionsbeiträge 127, University of Tübingen, School of Business and Economics.
    23. Domenico Delli Gatti & Corrado Di Guilmi & Mauro Gallegati & Simone Landini, 2012. "Reconstructing Aggregate Dynamics in Heterogeneous Agents Models. A Markovian Approach," Revue de l'OFCE, Presses de Sciences-Po, vol. 0(5), pages 117-146.

    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:spr:joevec:v:2:y:1992:i:3:p:233-65. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.