Incentive Stackelberg Games for Stochastic Linear Systems With $H_\infty$ Constraint

In this paper, incentive Stackelberg games with one leader and multiple followers are investigated for a class of stochastic linear systems with external disturbance. Unlike the existing ordinary Stackelberg games, the leader is required to design an incentive Stackelberg strategy set that can lead to the leader's team-optimal solution and the follower's Nash equilibrium, and attenuate the external disturbance in the system simultaneously. It is shown that the incentive Stackelberg strategy set is obtained by solving a set of the cross-coupled stochastic Riccati differential equations in a finite-horizon case and a set of the cross-coupled stochastic algebraic Riccati equations in an infinite-horizon case. Numerical examples are solved to demonstrate the effectiveness of the proposed incentive Stackelberg strategy set.