Three-level multi-leader-follower incentive Stackelberg differential game with <i>H</i> _∞ constraint

This paper is concerned with a three-level multi-leader-follower incentive Stackelberg game with H ∞ constraint. Based on H 2 / H ∞ control theory, we firstly obtain the worst-case disturbance and the team-optimal strategy by finding a closed-loop Nash equilibrium of the corresponding nonzero-sum stochastic differential game. The main objective is to establish an incentive Stackelberg strategy set of the three-level hierarchy in which the whole system achieves the top leader’s team-optimal solution and attenuates the external disturbance under H ∞ constraint. On the other hand, followers on the bottom two levels in turn attain their state feedback Nash equilibrium, ensuring incentive Stackelberg strategies while considering the worst-case disturbance. By convex analysis theory, maximum principle and decoupling technique, the three-level incentive Stackelberg strategy set is obtained. Finally, a numerical example is given to illustrate the existence of the proposed strategy set.