Stochastic perturbations for a duopoly Stackelberg model

In this paper, a duopoly Stackelberg model of competition on output with stochastic perturbations is proposed. Sufficient conditions for the existence and the uniqueness of global positive solution of the stochastic system are derived. For the stochastic Stackelberg model (SSM), the authors obtained some sufficient conditions for the globally asymptotical stability of the Nash equilibrium. When ignoring the stochastic perturbations, sufficient criteria for the corresponding deterministic Stackelberg model (DSM) is also obtained. In addition, by applying Milstein's numerical algorithm, we solve the stochastic differential model then plot the time-series diagram, which can help us deduce the change regulation of the output of two firms in the competition game. Finally, some discussions are given for the economic significance for the model. (C) 2019 Elsevier B.V. All rights reserved.