Dynamics of a Cournot Duopoly Game with Differentiated Goods Between Public and Private Firms

This paper investigates the dynamics of a nonlinear Cournot-type duopoly game with differentiated goods, linear demand and cost functions for two bounded rational players that have different objective functions. Specifically, the first player is a public company and cares about the social welfare and the second player is a private company which cares only about its own profit maximization. The game is modeled with a system of two difference equations. The stability analysis of the fixed points are analyzed and complex dynamic features including period doubling bifurcations of the unique Nash equilibrium is also investigated. Numerical simulations are carried out to show the complex behavior of the models' parameters. We show that a higher (lower) degree of the speed of adjustment and a lower (higher) degree of the parameter of product differentiation destabilize (stabilize) the economy. The chaotic features are justified numerically via computing Lyapunov numbers, sensitive dependence on initial conditions, bifurcation diagrams and strange attractors.