Continuous-Time Information-Mechanism Control

In a continuous-time stochastic Stackelberg differential game, a leader steers strategic followers through the information structure and a transfer mechanism, not the dynamics. We pose two problems, neither formulated as a control problem with strategic followers: information control, where the leader commits only to a disclosure policy, and information-mechanism control, which adjoins transfers. The first is equilibrium-constrained and admits no dynamic programming principle; the second is tractable, and the transfer is why: alignment makes the lower level a potential game, collapsing the bilevel problem to one stochastic control problem with an exact first-order condition. Disclosure precision becomes a control input and the belief a controlled state obeying a Riccati equation. The latent environment is a jump-diffusion whose belief filter is exactly finite-dimensional under publicly observed epochs. A marginal-contribution transfer makes truthful reporting dominant and efficient action the Nash response. Equilibrium feedback is saturated on strictly convex components and bang-bang on linear ones, hence discontinuous. The master value is the unique viscosity solution of a partial integro-differential Hamilton-Jacobi-Bellman equation whose nonlocal term carries the epochs; verification holds without smoothness, and semiconcavity makes the switching set null, giving a well-posed Filippov closed loop. Instantiated on multi-area power systems, the levers are complements under a one-factor common shock. Calibrated to 2021 Winter Storm Uri, coupling removes 7.4% of social cost relative to autarky, rising to 35% at a 10-gigawatt tie, and disclosure is worth 8.7%; under a European renewable-drought calibration it is worth 37% under autarky and 48% under coupling.