Mathematical properties of a discontinuous Cournot–Stackelberg model

The object of this work is to perform the global analysis of a recent duopoly model which couples the two points of view of Cournot and Stackelberg and . 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 investigated 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.