Complex dynamics of a duopoly game model with bounded rationality and heterogeneous product

In this paper, the author first introduces studies on duopoly game models and points out the deficiencies of these models. Then a new duopoly game model with bounded rationality and differentiated product is constructed. The author then analyzes the complex dynamics of this model, giving the condition which ensures the existence of Nash equilibrium, showing that the extent of product substitution and the speeds of production adjustment of these firms can determine whether the game can reach Nash equilibrium or not, even lead to chaos, So the firms in the duopoly game have to adjust their reaction speeds continuously, and manage to make the product substitution factor small enough in order to maintain the stability of Nash equilibrium to get the maximum profits, and avoid the occurrence of chaos.