Infinite-horizon multi-leader-follower incentive stackelberg games for linear stochastic systems with H∞ constraint

In this paper, an infinite-horizon incentive Stackelberg game with multiple leaders and multiple followers is investigated for a class of linear stochastic systems with H
_∞
constraint. In this game, an incentive structure is developed in such a way that leaders achieve Nash equilibrium attenuating the disturbance under H
_∞
constraint. Simultaneously, followers achieve their Nash equilibrium ensuring the incentive Stackelberg strategies of the leaders while the worst-case disturbance is considered. In our research, it is shown that by solving some cross-coupled stochastic algebraic Riccati equations (CCSAREs) and matrix algebraic equations (MAEs) the incentive Stackelberg strategy set can be obtained. Finally, to demonstrate the effectiveness of our proposed scheme, a numerical example is solved.