Incentive feedback Stackelberg strategy for the discrete-time stochastic systems

Abstract

The paper is devoted to designing an incentive Stackelberg strategy for the discrete-time stochastic systems. Most of the existing works are about the deterministic systems and the continuous-time stochastic systems. Although many methods have been used to help the leader to attain his team-optimal value, due to the involvement of the conditional expectation, the design of the incentive Stackelberg strategy for the discrete-time stochastic systems is more difficult and complicated. In this paper, this problem is studied for both the finite horizon case and the infinite horizon situation. Also, the mean-square stability is guaranteed by the follower. In addition, for the infinite horizon case, the specific algorithm procedure is put forward to obtain the incentive feedback Stackelberg strategy conveniently. At last, two examples are given to verify the effectiveness of the proposed algorithm procedure.