Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Information

In this work, the dynamics of a Cournot type duopoly game are studied, where the two players produce and offer differentiated products on a common market. The two firms (players) use a quadratic cost function and follow different strategies. The first player is considered as a bounded rational player while the second player is naïve. We suppose a separate case for each player that one player has information about the next time production of its opponent. In an algebraic way the equilibrium positions of the discrete dynamical system of the game are found, as well as a proposition is formulated that constitutes the stability condition of the Nash Equilibrium. Some numerical simulations such as bifurcation diagrams, strange attractors, graphs of Lyapunov numbers and sensitivity analysis on the initial conditions of the dynamical system are presented focusing on the adjustment speed parameter and the products’ differentiation parameter for specific values of the other parameters, in order to confirm the algebraic results of the game and to visualize the chaotic behavior of the system when these two basic parameters take values outside their stability region. Finally, a chaos control mechanism is presented for the values of these two parameters that cause it to appear.