Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition

E. Droste, Cars Hommes and Jan Tuinstra

No 99-04, CeNDEF Working Papers from Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance

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.

Keywords: Evolutionary game theory; heterogeneous behavioural rules; Cournot competition; homoclinic bifurcation theory. (search for similar items in EconPapers)
Date: 1999
New Economics Papers: this item is included in nep-evo, nep-gth and nep-mic
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Citations: View citations in EconPapers (8)

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Journal Article: Endogenous fluctuations under evolutionary pressure in Cournot competition (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:ams:ndfwpp:99-04

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