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The Master Equation Approach to Nonlinear Economics

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  • 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
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    Cited by:

    1. Helbing, Dirk & Kern, Daniel, 2000. "Non-equilibrium price theories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 259-268.
    2. 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.
    3. 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.
    4. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.
    5. 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.
    6. 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.
    7. 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.
    8. Verspagen, Bart, 1998. "Special issue on the evolutionary analysis of innovation," Structural Change and Economic Dynamics, Elsevier, vol. 9(1), pages 1-3, March.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. 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.
    16. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    17. 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.
    18. 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.
    19. Hawkins, Raymond J., 2011. "Lending sociodynamics and economic instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4355-4369.
    20. 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.
    21. 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.
    22. 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.
    23. 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).

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