A Stochastic Multiple-Leader-Follower Incentive Stackelberg Strategy for Markov Jump Linear Systems

An incentive Stackelberg game for a class of Markov jump linear stochastic systems with multiple leaders and followers is investigated in this letter. An incentive structure is developed that allows the leader's Nash equilibrium to be achieved. In the game, the followers are assumed to behave in two ways under the leader's incentive strategy set. One involves achieving a Pareto-optimal solution, and the other involves achieving Nash equilibrium. Consequently, it can be verified that irrespective of how the followers behave, they can be induced to achieve the leader's Nash equilibrium by using a corresponding incentive strategy set. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati-type equations. As another important contribution, a novel concept of incentive possibility is proposed for a special case. In order to demonstrate the effectiveness of the proposed scheme, a numerical example is solved.