Multi-leader-follower Incentive Stackelberg game for Infinite-Horizon Markov Jump Linear Stochastic Systems with H∞ Constraint

An incentive Stackelberg game for a class of Markov jump linear stochastic systems (MJLSS) with multiple leaders and followers under H-infinity constraint is investigated. The main objective is to develop an incentive structure of a two-level hierarchy in which the leaders achieve state feedback Nash equilibrium, attenuating the external disturbance under an H-infinity constraint. On the other hand, followers attain their state feedback Nash equilibrium/Pareto optimality, ensuring incentive Stackelberg strategies of the leaders while considering the worst-case disturbance. As a result, regardless of the behavior of the followers non-cooperative/cooperative, they are induced by the incentive strategy to achieve Nash equilibrium of the leaders. It is shown that the proposed strategy set can be obtained by solving cross-coupled stochastic algebraic Riccati equations (SAREs). Furthermore, as another important contribution, a design of a mode independent incentive strategy set is developed in case the current mode cannot be observed accurately. A simple numerical example demonstrates the existence of the proposed strategy set.