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Mathematical Properties of a Combined Cournot-Stackelberg model

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Author Info

  • 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.

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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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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 1007.

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Length: 27 pages
Date of creation: 2010
Date of revision: 2010
Handle: RePEc:urb:wpaper:10_07

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Web page: http://www.econ.uniurb.it/
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Related research

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

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Cited by:
  1. Fabio Lamantia, 2011. "A Nonlinear Duopoly with Efficient Production-Capacity Levels," Computational Economics, Society for Computational Economics, vol. 38(3), pages 295-309, October.

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