  We analyze many-sender Bayesian persuasion games where receiver can contract
their action on senders' choices of Blackwell experiment and realized signals.
We characterize robust mechanisms: those that induce the same joint
distributions of actions and senders' private types for all possible prior
beliefs. These mechanisms take a simple form: they (1) incentivize maximally
informative experiments, and (2) depend only on the induced posterior. We prove
a grim-trigger-like principle for unilateral deviations, and show robustness is
pinned down by a finite set of linear inequalities. We apply our model to
allocation problems with either type-dependent outside options or allocation
externalities and identify conditions where the efficient outcome is robust.
Finally, we uncover a novel justification for deferred acceptance via
informational incentives in two-sided matching when school preferences depend
on students' unknown ability.
