Continuous pricing in oligopoly

The continuous dynamics of competing firms in an oligopoly market is studied in terms of the Cournot theory. The Bogoyavlensky qualitative methods of multidimensional dynamical systems (the maximally nondegenerate compactification) are used in the analysis of the system where xi and πi(x1, …, xN) is output and profit of the ith firm, respectively. The exact solutions of this model are found. We show that the number of critical points and their character are preserved under changing of the system dimension N. The phase portrait with the Poincaré compactification for the duopoly model is constructed. We also show the structural stability of this model.