Endogenous fluctuations under evolutionary pressure in Cournot competition
AbstractAn 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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Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 40 (2002)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/locate/inca/622836
Other versions of this item:
- Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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- Novshek, William., 1984.
"On the Existence of Cournot Equilibrium,"
517, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
- 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.
- 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.
- 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.
- 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.
- D. Stahl, 2010.
"Evolution of Smart n Players,"
Levine's Working Paper Archive
401, David K. Levine.
- William A. Brock & Cars H. Hommes, 1997.
"A Rational Route to Randomness,"
Econometric Society, vol. 65(5), pages 1059-1096, September.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- 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.
- Seade, Jesus, 1980. "The stability of cournot revisited," Journal of Economic Theory, Elsevier, vol. 23(1), pages 15-27, August.
- 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.
- Corchon, Luis C. & Mas-Colell, Andreu, 1996.
"On the stability of best reply and gradient systems with applications to imperfectly competitive models,"
Elsevier, vol. 51(1), pages 59-65, April.
- Corchón, Luis C. & Mas-Colell, A., . "On the stability of best reply and gradient systems with application to imperfectly competitive models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3812, Universidad Carlos III de Madrid.
- 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.
- 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.
- 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.
- 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.
- 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.
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