Before revision:  In equilibrium, the principal's patience is the key determinant of her information provision: the lower her discount rate, the more eagerly she funds. When she is sufficiently patient, her information provision and value function are well-approximated by the 'Bayesian persuasion' model. If the conflict of interest is purely belief-based and information is valuable, then she provides full information if she is patient. We also obtain a sharp characterisation of the principal's value function. Our proofs rely on a novel dynamic programming principle rooted in the theory of viscosity solutions of differential equations .
After revision:  Using a novel 'viscosity' dynamic programming principle, we characterise the sender's equilibrium value function and information provision. We show that the graduality constraint inhibits information provision relative to unconstrained persuasion. The gap can be substantial, but closes as the constraint slackens. Contrary to unconstrained persuasion, less-than-full information may be provided even if players have aligned preferences but different prior beliefs .