Incentive feedback Stackelberg strategy for the mean‐field type Itô stochastic systems with Poisson jumps

Abstract This paper proposes an incentive Stackelberg strategy for the mean‐field type Itô stochastic systems with Poisson jumps in finite horizon and infinite horizon, respectively. Unlike the regular Stackelberg strategy, the obtained incentive Stackelberg strategy allows the leader to achieve his desired goal, that is, attaining his global optimum. Also, the mean‐square stability of the system is investigated, and it can be achieved by the follower. In addition, an algorithm procedure is introduced to derive the incentive feedback Stackelberg strategy in an infinite horizon. Finally, two examples are provided to highlight the effectiveness of the proposed results.