Dynamic investigations in a Stackelberg model with differentiated products and bounded rationality

This work focuses on a Stackelberg duopoly game characterized by firms with differentiated products and bounded rationality. Both firms adopt myopic mechanism to update their production decisions in each discrete period. For the purpose of stressing hierarchy between both firms, the leader firm is supposed to estimate marginal profit by only thinking over his own interfering factors. Since global stability analysis of Nash equilibrium point becomes desirable in complex behaviors research, we cover it as well besides local stability. Numerical simulations are carried out to verify some essential appearances of previous theoretical analyses. Such aspects include maximum Lyapunov exponent, strange attractor, basin of attraction and sensitivity on initial conditions. In addition, we calculate fractal dimension of the non-integral dimension shapes in chaotic state. As to the chaos emerged under certain conditions, effective control method has been utilized to force them back towards stability. (c) 2022 Elsevier B.V. All rights reserved.