Endogenous fluctuations under evolutionary pressure in Cournot competition
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.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
- 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.
- 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.
- William A. Brock & Cars H. Hommes, 1997.
"A Rational Route to Randomness,"
Econometric Society, vol. 65(5), pages 1059-1096, September.
- Gale, D. & Rosental, R.W., 1996.
"Experimentation, Imitation, and Stochastic Stability,"
65, Boston University - Industry Studies Programme.
- Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
- Douglas Gale & Robert W. Rosenthal, 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 0065, Boston University - Industry Studies Programme.
- William Novshek, 1985.
"On the Existence of Cournot Equilibrium,"
Review of Economic Studies,
Oxford University Press, vol. 52(1), pages 85-98.
- D. Stahl, 2010.
"Evolution of Smart n Players,"
Levine's Working Paper Archive
401, David K. Levine.
- Cox, James C. & Walker, Mark, 1998. "Learning to play Cournot duopoly strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 36(2), pages 141-161, August.
- F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," Review of Economic Studies, Oxford University Press, vol. 29(4), pages 329-331.
- Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
- Karl H. Schlag, 1995.
"Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits,"
Discussion Paper Serie B
361, University of Bonn, Germany, revised Mar 1996.
- Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
- Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
- Yokoo, Masanori, 2000. "Chaotic dynamics in a two-dimensional overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 909-934, June.
- de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
- Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-22, February.
- Seade, Jesus, 1980. "The stability of cournot revisited," Journal of Economic Theory, Elsevier, vol. 23(1), pages 15-27, August.
- K. Schlag, 2010.
"Why Imitate, and if so, How? Exploring a Model of Social Evolution,"
Levine's Working Paper Archive
454, David K. Levine.
- Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
- Ariel Rubinstein, 1997.
"Finite automata play the repeated prisioners dilemma,"
Levine's Working Paper Archive
1639, David K. Levine.
- Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:40:y:2002:i:2:p:232-269. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.