  We consider a game of persuasion with evidence between a sender and a
receiver. The sender has private information. By presenting evidence on the
information, the sender wishes to persuade the receiver to take a single action
(e.g., hire a job candidate, or convict a defendant). The sender's utility
depends solely on whether or not the receiver takes the action. The receiver's
utility depends on both the action as well as the sender's private information.
We study three natural variations. First, we consider sequential equilibria of
the game without commitment power. Second, we consider a persuasion variant,
where the sender commits to a signaling scheme and then the receiver, after
seeing the evidence, takes the action or not. Third, we study a delegation
variant, where the receiver first commits to taking the action if being
presented certain evidence, and then the sender presents evidence to maximize
the probability the action is taken. We study these variants through the
computational lens, and give hardness results, optimal approximation
algorithms, as well as polynomial-time algorithms for special cases. Among our
results is an approximation algorithm that rounds a semidefinite program that
might be of independent interest, since, to the best of our knowledge, it is
the first such approximation algorithm for a natural problem in algorithmic
economics.
