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Mathematical Properties of a Combined Cournot-Stackelberg model

Author

Listed:
  • Fabio Tramontana

    () (Department of Economics, University of Ancona, Italy)

  • Laura Gardini

    () (Department of Economics and Quantitative Methods, University of Urbino, Italy)

  • Tönu Puu

    () (CERUM, Umeå University, SE-90187 Umeå, Sweden)

Abstract

The object of this work is to perform the global analysis of a new duopoly model which couples the two points of view of Cournot and Stackelberg. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigates as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which di¤er significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.

Suggested Citation

  • Fabio Tramontana & Laura Gardini & Tönu Puu, 2010. "Mathematical Properties of a Combined Cournot-Stackelberg model," Working Papers 1007, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2010.
  • Handle: RePEc:urb:wpaper:10_07
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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_10_07.pdf
    File Function: First version, 2010
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    Cited by:

    1. Fabio Lamantia & Mario Pezzino, 2017. "Dynamic analysis of discontinuous best response with innovation," The School of Economics Discussion Paper Series 1708, Economics, The University of Manchester.
    2. Fabio Lamantia, 2011. "A Nonlinear Duopoly with Efficient Production-Capacity Levels," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 295-309, October.

    More about this item

    Keywords

    Cournot-Stackelberg duopoly; Isoelastic demand function; Discontinuous reaction functions; Multistability; Border-collision bifurcations.;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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