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Oligopoly games with Local Monopolistic Approximation


  • Bischi, Gian Italo
  • Naimzada, Ahmad K.
  • Sbragia, Lucia


We propose a repeated oligopoly game where quantity setting firms have incomplete knowledge of the demand function of the market in which they operate. At each time step they solve a profit maximization problem by using a subjective approximation of the demand function based on a local estimate its partial derivative, computed at the current values of prices and outputs, obtained through market experiments. At each time step they extrapolate such local approximation by assuming a linear demand function and ignoring the effects of the competitors outputs. Despite a so rough approximation, that we call "Local Monopolistic Approximation" (LMA), the repeated game may converge to a Nash equilibrium of the true oligopoly game, i.e. the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Sufficient conditions for the local stability of Nash Equilibria are given. In the particular case of an isoelastic demand function, we show that the repeatead game based on LMA always converges to a Nash equilibrium, both with linear and quadratic cost functions. This stability result is compared with "best reply" dynamics, obtained under the assumption of isoelastic demand (fully known by the players) and linear costs.
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  • Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
  • Handle: RePEc:eee:jeborg:v:62:y:2007:i:3:p:371-388

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    References listed on IDEAS

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    Cited by:

    1. Ahmad Naimzada & Fabio Tramontana, 2011. "Double route to chaos in an heterogeneous triopoly game," Quaderni di Dipartimento 149, University of Pavia, Department of Economics and Quantitative Methods.
    2. repec:pts:journl:y:2017:i:1:p:11-22 is not listed on IDEAS
    3. Naimzada, Ahmad & Ricchiuti, Giorgio, 2011. "Monopoly with local knowledge of demand function," Economic Modelling, Elsevier, vol. 28(1), pages 299-307.
    4. Marcelo J. Villena & Axel A. Araneda, 2015. "Dynamics and Stability in Retail Competition," Papers 1510.04550,, revised Mar 2016.
    5. 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.
    6. Kopányi, Dávid, 2017. "The coexistence of stable equilibria under least squares learning," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 277-300.
    7. repec:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0503-y is not listed on IDEAS
    8. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. repec:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0501-0 is not listed on IDEAS
    10. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2016. "Evolutionary Competition between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," THEMA Working Papers 2016-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    11. Kamalinejad, Howra & Majd, Vahid Johari & Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2010. "Cournot games with linear regression expectations in oligopolistic markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1874-1885.
    12. Villena, Marcelo J. & Araneda, Axel A., 2017. "Dynamics and stability in retail competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 37-53.
    13. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    14. repec:eee:apmaco:v:271:y:2015:i:c:p:259-268 is not listed on IDEAS
    15. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," MPRA Paper 62300, University Library of Munich, Germany.
    16. Arranz Sombría, M. Rosa, 2011. "Cooperación en modelos de Cournot con información incompleta/Cooperation in Cournot’s Models with Incomplete Information," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 397(18á)-39, Abril.
    17. Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2011. "Decision making in dynamic stochastic Cournot games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1202-1217.
    18. 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.
    19. 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.
    20. Georges Sarafopoulos, 2015. "On the complex dynamics of a bounded rational monopolist model," International Journal of Business and Economic Sciences Applied Research (IJBESAR), Eastern Macedonia and Thrace Institute of Technology (EMATTECH), Kavala, Greece, vol. 8(1), pages 113-120, August.
    21. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    22. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.

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