Dynamics and Chaos Control of a Cournot Game with Heterogeneous Expectations, Asymmetric Information and Social Welfare

The present study extends previous works, assumes a Cournot-type duopoly game where the players produce differentiated goods and focus on players with asymmetric information. The players take into account not only their profits, but also a percentage of social welfare which is different for each player. The first player acts like a naïve, while the other as a bounded rational player, who has information about production decision of the other player during the next period. The existence and stability of equilibria of this system is examined. Numerical simulations, through bifurcation diagrams, strange attractors, Lyapunov numbers and sensitive dependence on initial conditions, show the effect of the speed of adjustment of the bounded rational player on the dynamics of the system. The speed of adjustment of the bounded rational player may change the stability of the Nash equilibrium and cause a structure to behave chaotically. After that, is examined the impact of the parameter of degree differentiation of the products in the system. Finally, an attempt is made to control the chaotic behavior.