Linear-Quadratic Stochastic Stackelberg Differential Games for Jump-Diffusion Systems Under General Partial Information

Abstract

This paper studies the linear-quadratic stochastic Stackelberg differential game for jumpdiffusion systems under partial information. In our problem setup, given the complete information F, the partial information of the leader and the follower is constructed by H1 ⊂ F and H2 ⊂ F, respectively, where Hˆ := H1 ∩ H2 ̸= ∅ captures their common information. Our paper extends the problem with asymmetric information in [1], which can be regarded as a special case of this paper with H2 ⊂ H1 and Hˆ = H2. Indeed, unlike [1], due to the presence of Hˆ , it is necessary to deal with Hˆ separately to obtain the Stackelberg equilibrium. Through the generalized maximum principles and four-step schemes of the leader and the follower, we show that the overall feedback-type Stackelberg equilibrium can be represented by the filtering state processes with respect to (H1, H2, Hˆ ).