CONTINUOUS PRICING IN OLIGOPOLY

The continuous dynamics of competing firms in an oligopoly market is s tudied in terms of the Cournot theory. The Bogoyavlensky qualitative m ethods of multidimensional dynamical systems (the maximally nondegener ate compactification) are used in the analysis of the system dx(i)/dt = d pi(i)/dx(i), i = 1, ..., N where x(i) and pi(i)(x(1), ..., x(N)) i s output and profit of the ith firm, respectively. The exact solutions of this model are found. We show that the number of critical points a nd their character are preserved under changing of the system dimensio n N. The phase portrait with the Poincare compactification for the duo poly model is constructed. We also show the structural stability of th is model. Copyright (C) 1996 Elsevier Science Ltd.