Mathematical Properties of a Combined Cournot-Stackelberg model

Posted by D. Daniel Sokol

Fabio Tramontana (Department of Economics, University of Ancona, Italy), Laura Gardini (Department of Economics and Quantitative Methods, University of Urbino, Italy), and Tönu Puu (CERUM, Umeå University) explore Mathematical Properties of a Combined Cournot-Stackelberg model.

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 differ 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.