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Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition

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Author Info
Droste, E.
Hommes, C.H. () (Universiteit van Amsterdam)
Tuinstra, J. () (Universiteit van Amsterdam)

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Abstract

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioural rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioural rule are updated according to the replicator equation with noise. The long-run behaviour of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the rational rule and the best-reply rule. We show that, if the best-reply rule is unstable, a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases (that is, as the noise level decreases), implying bifurcation routes to complicated dynamics and strange attractors.

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Publisher Info
Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 99-04.

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Date of creation: 1999
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Handle: RePEc:ams:ndfwpp:99-04

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
Web page: http://www.fee.uva.nl/cendef/
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Related research
Keywords: Evolutionary game theory; heterogeneous behavioural rules; Cournot competition; homoclinic bifurcation theory.;

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  1. Oddvar M. Kaarbøe & Alexander F. Tieman, 1999. "Equilibrium Selection in Games with Macroeconomic Complementarities," Tinbergen Institute Discussion Papers 99-096/1, Tinbergen Institute. [Downloadable!]
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  2. Brock, W.A. & Dindo, P.D.E. & Hommes, C.H., 2005. "Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont," CeNDEF Working Papers 05-15, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  3. Diks, C.G.H. & Dindo, P.D.E., 2006. "Informational differences and learning in an asset market with boundedly rational agents," CeNDEF Working Papers 06-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
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  4. Hommes, C.H. & Huang, H. & Wang, D., 2002. "A Robust Rational Route to in a Simple Asset Pricing Model (revised March 2004)," CeNDEF Working Papers 02-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  5. Schipper, Burkhard, 2008. "Imitators and Optimizers in Cournot Oligopoly," Working Papers 05-37, University of California at Davis, Department of Economics. [Downloadable!]
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  6. Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics 02_01, University of Dortmund, Department of Economics. [Downloadable!]
  7. Andrew F. Daughety, 2006. "Cournot Competition," Working Papers 0620, Department of Economics, Vanderbilt University. [Downloadable!]
  8. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute. [Downloadable!]
  9. Dindo, P.D.E. & Tuinstra, J., 2006. "A Behavioral Model for Participation Games with Negative Feedback," CeNDEF Working Papers 06-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
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