Linear-Quadratic Stochastic Stackelberg Games of N Players for Time-Delay Systems and Related FBSDEs

Motivated by the multi-scheme supply chain problem, a linear-quadratic generalized Stackelberg game for time-delay is studied, in which the multi-level hierarchy structure with delay is involved. With the help of the continuity method, we first establish the unique solvability of nonlinear anticipated forward–backward stochastic delayed differential equations with a multi-level self-similar domination-monotonicity structure. Based on it, we derive the Stackelberg equilibrium in this framework. By the theoretical results, a corporate social responsibility problem is studied in the view of a multi-scheme supply chain problem, some simulations are also presented to illustrate the Stackelberg equilibrium in a special case.