Exploring complex dynamics in a Stackelberg Cournot duopoly game model

In this study, we investigate the dynamics of a Cournot duopoly game model with bounded rational players, incorporating a leader-follower mechanism where the first player acts as a leader and the second as a follower, aware of the leader's production. We examine the existence and stability of all fixed points in the model and use center manifold and bifurcation theory to analyze the occurrence and direction of period- doubling and Neimark-Sacker bifurcations at the positive fixed point. To control bifurcation and chaos, feedback control and hybrid control methods are applied. Numerical examples are provided to confirm our theoretical results and reveal the model's complex dynamics. Our results highlight the critical role of the leader's strategic decisions, particularly the adjustment speed parameter v( 1 ), in driving the system from stability to chaos, affecting both firms and leading to significant shifts in market dynamics.