Linear-quadratic stochastic Stackelberg differential games with asymmetric information for systems driven by multi-dimensional jump-diffusion processes

Abstract

We consider the linear-quadratic stochastic leader-follower Stackelberg differential game for jump-diffusion systems with asymmetric information. In our problem setup, given complete information F, leader and follower have access to partial information (filtration) G1⊂F and G2⊂F, respectively, where G2⊂G1 captures asymmetric information. Our paper can be viewed as an extension of the complete information (G2=G1=F) in [15] to the problem with partial and asymmetric information. By generalizing the stochastic maximum principles and four-step schemes of [15], we obtain the state-feedback representation of the (open-loop type) Stackelberg equilibrium for the leader and the follower in terms of the coupled integro-type Riccati differential equations and the filtering (state) processes with respect to G2 and G1. Indeed, due to the partial and asymmetric information nature, we have to identify new types of the four-step schemes and develop different approaches to obtain the (filtering-based) state-feedback type Stackelberg equilibrium.