The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

GLOBALIZATION OF A LOCAL MARKET DYNAMICS ONTO AN INFINITE CHAIN OF LOCAL MARKETS

  • Published : 2009.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to extend and globalize the Walrasian evolutionary cobweb model in an independent single local market of Brock and Hommes ([3]), to the case of the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. In the case of decreasing demands and increasing supplies with a weighted average of rational and naive predictors, we investigate, via the methods of Lattice Dynamical System, the spatial-temporal behaviors of global market dynamics and show that some kind of bounded dynamics of global market do exist and can be controlled by using the parameters in the model.

Keywords

References

  1. Afraimovich, V.S. & Bunimovich, L.A.: Simplest structures in coupled map lattices and their stability. Preprint in GIT.
  2. Aranson, I.S.; Afraimovich, V.S. & Rabinovich, M.I. : Stability of spatially homogeneous chaotic regimes in unidirectional chains. Nonlinearity 3 (1990), 639-651. https://doi.org/10.1088/0951-7715/3/3/006
  3. Brock, W.A. & Hommes, C.H.: A Rational Route to Randomness. Econometrica 65 (1997), no. 5, 1059-1095. https://doi.org/10.2307/2171879
  4. Brock, W.A. & Hommes, C.H. : Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model. Journal of Economic Dynamics and Control 22 (1998), 1235-1274. https://doi.org/10.1016/S0165-1889(98)00011-6
  5. Brock, W.A.; Hommes, C.H. & Wagner, F.O.O.: Evolutionary dynamics in markets with many trader types. Journal of Mathematical Economics 41 (2005), 7-42. https://doi.org/10.1016/j.jmateco.2004.02.002
  6. Bunimovich, L.A. et al: Trivial Maps. Chaos 2 (1992).
  7. Bunimovich, L.A. & Sinai, Y.G.: Spacetime Chaos in Coupled Map Lattices. Nonlinearity 1 (1988), 491-516 https://doi.org/10.1088/0951-7715/1/4/001
  8. Hommes, C.H.: On the consistency of backward-looking expectations: The case of the cobweb. Journal of Economic Behavior & Organization 33 (1998), 333-362. https://doi.org/10.1016/S0167-2681(97)00062-0
  9. Kaneko, K.: Theory and applitions of coupled map lattices. John-Wiley and Sons (1993).
  10. Waller, I. & Kapral, R.: Spatial and Temporal Structure in Systems of Coupled Non­linear Oscillations. Physical Review A 30 (1984), 2047-2055. https://doi.org/10.1103/PhysRevA.30.2047