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This paper is intended to investigate the dynamics of heterogeneous Cournotduopoly games, where the first players adopt identical gradient adjustmentmechanisms but the second players are endowed with distinct rationality levels.Based on tools of symbolic computations, we introduce a new approach and use itto establish rigorous conditions of the local stability for these models. Weanalytically investigate the bifurcations and prove that the period-doublingbifurcation is the only possible bifurcation that may occur for all theconsidered models. The most important finding of our study is regarding theinfluence of players' rational levels on the stability of heterogeneousduopolistic competition. It is derived that the stability region of the modelwhere the second firm is rational is the smallest, while that of the one wherethe second firm is boundedly rational is the largest. This fact iscounterintuitive and contrasts with relative conclusions in the existingliterature. Furthermore, we also provide numerical simulations to demonstratethe emergence of complex dynamics such as periodic solutions with differentorders and strange attractors.

Influence of rationality levels on dynamics of heterogeneous Cournot duopolists with quadratic costs