Information design and sequential screening with ex post participation constraint

We study a principal--agent model. The parties are symmetrically informed at first; the principal then designs the process by which the agent learns his type and, concurrently, the screening mechanism. Because the agent can opt out of the mechanism ex post, it must leave him with nonnegative rents ex post. We characterize the profit-maximizing mechanism. In that optimal mechanism, learning proceeds in continuous time and, at each moment, the agent learns a lower bound on his type. For each type, there is one of two possible outcomes: the type is allocated the efficient quantity or is left with zero rents ex post.