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Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition

  • Droste, E.
  • Hommes, C.H.


    (Universiteit van Amsterdam)

  • Tuinstra, J.


    (Universiteit van Amsterdam)

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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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
Date of revision:
Handle: RePEc:ams:ndfwpp:99-04
Contact details of provider: 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
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  1. D. Stahl, 2010. "Evolution of Smart n Players," Levine's Working Paper Archive 401, David K. Levine.
  2. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  3. Droste, E.J.R. & Tuinstra, J., 1998. "Evolutionary Selection of Behavioral Rules in a Cournot Model : A Local Bifurcation Analysis," Discussion Paper 1998-86, Tilburg University, Center for Economic Research.
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  13. Corchon, Luis C. & Mas-Colell, Andreu, 1996. "On the stability of best reply and gradient systems with applications to imperfectly competitive models," Economics Letters, Elsevier, vol. 51(1), pages 59-65, April.
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