IEEE Trans Cybern. 2019 Apr;49(4):1463-1474. doi: 10.1109/TCYB.2018.2804920. Epub 2018 Feb 26.
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.
本文针对一类具有外部干扰的随机线性系统，研究了具有一个领导者和多个跟随者的激励 Stackelberg 博弈。与现有的普通 Stackelberg 博弈不同，领导者需要设计一个激励 Stackelberg 策略集，既能使领导者的团队达到最优解，又能使跟随者达到纳什均衡，并同时衰减系统中的外部干扰。结果表明，在有限时域内，激励 Stackelberg 策略集通过求解一组交叉耦合随机 Riccati 微分方程得到；在无限时域内，通过求解一组交叉耦合随机代数 Riccati 方程得到。数值算例验证了所提出的激励 Stackelberg 策略集的有效性。
