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Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games


  • G.‐I. Bischi
  • M. Gallegati
  • A. Naimzada


In this paper, we investigate the question of whether the assumption of the “representativeagent”, often made in economic modeling, is innocuous or whether it may be misleadingunder certain circumstances. In order to obtain some insight into this question, two dynamicCournot duopoly games are considered, whose dynamics are represented by discrete‐timedynamical systems. For each of these models, the dynamical behavior of the duopoly systemwith identical producers is compared to that with quasi‐identical ones, in order to study theeffects of small heterogeneities between the players. In the case of identical players, suchdynamical systems become symmetric, and this implies that synchronized dynamics can beobtained, governed by a simpler one‐dimensional model whose dynamics summarizes thecommon behavior of the two identical players. In both the examples, we show that a negligibledifference between the parameters that characterize the two producers can give dynamicevolutions that are qualitatively different from that of the symmetric game, i.e. a breakingof the symmetry can cause a noticeable effect. The presence of such bifurcations suggeststhat economic systems with quasi‐identical agents may evolve quite differently from systemswith truly identical agents. This contrasts with the assumption, very common in the economicliterature, that small heterogeneities of agents do not matter too much. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
  • Handle: RePEc:spr:annopr:v:89:y:1999:i:0:p:252-271:10.1023/a:1018931824853
    DOI: 10.1023/A:1018931824853

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    Cited by:

    1. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    2. repec:eee:apmaco:v:312:y:2017:i:c:p:169-176 is not listed on IDEAS
    3. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    4. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    5. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," MPRA Paper 37834, University Library of Munich, Germany.
    6. Luciano Fanti & Luca Gori, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," Discussion Papers 2011/120, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    7. repec:eee:apmaco:v:321:y:2018:i:c:p:333-348 is not listed on IDEAS
    8. Antoci, Angelo & Naimzada, Ahmad & Sodini, Mauro, 2009. "Strategic interactions and heterogeneity in a overlapping generations model with negative environmental externalities," MPRA Paper 18221, University Library of Munich, Germany.
    9. repec:eee:apmaco:v:336:y:2018:i:c:p:193-205 is not listed on IDEAS
    10. Tomasz Dubiel-Teleszyński, 2010. "Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 2(2), pages 95-116, March.
    11. repec:eee:apmaco:v:281:y:2016:i:c:p:1-15 is not listed on IDEAS
    12. repec:eee:apmaco:v:335:y:2018:i:c:p:278-291 is not listed on IDEAS
    13. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    14. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.

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