Stochastic Stackelberg Games with a Jump-Diffusion Follower: Existence, Verification, and a Fixed-Point Algorithm
Coupled HJB-Isaacs analysis under monotone stopping
We study a continuous-time Stackelberg game in which a leader controls the drift of a state process and a representative follower, modeled as a jump-diffusion, chooses an exit time. We prove existence of a unique viscosity-solution equilibrium pair for the coupled HJB-Isaacs / free-boundary system, establish a verification theorem in viscosity sense whenever the follower’s optimal stopping region is monotone in the state ordering, and provide a fixed-point iteration on the value-function pair that converges geometrically. For Kou-distributed jumps with a linear leader payoff we derive a semi-closed-form representation via the resolvent operator $\mathscr{R}_q$ and verify the algorithm against this benchmark.