  A sender commits to an experiment to persuade a receiver. Accounting for the
sender's experiment-choice incentives, and not presupposing a receiver
tie-breaking rule when indifferent, we characterize when the sender's
equilibrium payoff is unique and so coincides with her "Bayesian persuasion"
value. A sufficient condition in finite models is that every action which is
receiver-optimal at some belief is uniquely optimal at some other belief -- a
generic property. We similarly show the equilibrium sender payoff is typically
unique in ordered models. In an extension, we show uniqueness generates
robustness to imperfect sender commitment.
