Dynamics of a duopoly game model with bounded rational players

This paper modeled a duopoly game, whose dynamics were investigated under the assumption of bounded rationality. Then the stability and the attraction basin of Nash equilibrium point were studied by using Jury´s criteria and numerical simulations, respectively. The results showed that the local stability region of Nash equilibrium point would shrink when the ratio of marginal costs increased. The attraction basin of Nash equilibrium point would shrink greatly and become irregular when the combination value of output adjustment speeds were close to the boundary of local stability region of Nash equilibrium point. It could be concluded that the locally asymptotical stability of Nash equilibrium point could be guaranteed when the combination values of output adjustment speeds were inside the local stability region and the initial values were inside the basin of attraction of Nash equilibrium point.