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Bayesian persuasion studies how an informed sender should partially discloseinformation so as to influence the behavior of self-interested receivers. Inthe last years, a growing attention has been devoted to relaxing the assumptionthat the sender perfectly knows receiver's payoffs. The first crucial steptowards such an achievement is to study settings where each receiver's payoffsdepend on their unknown type, which is randomly determined by a knownfinite-supported probability distribution. This begets considerablecomputational challenges, as computing a sender-optimal signaling scheme isinapproximable up to within any constant factor. In this work, we circumventthis issue by leveraging ideas from mechanism design. In particular, weintroduce a type reporting step in which the receiver is asked to report theirtype to the sender, after the latter has committed to a menu defining asignaling scheme for each possible receiver's type. We prove that, with asingle receiver, the addition of this type reporting stage makes the sender'scomputational problem tractable. Then, we extend our framework to settings withmultiple receivers, focusing on the case of no inter-agent externalities andbinary actions. We show that it is possible to find a sender-optimal solutionin polynomial-time by means of the ellipsoid method, given access to a suitablepolynomial-time separation oracle. This can be implemented for supermodular andanonymous sender's utility functions. As for the case of submodular sender'sutility functions, we first approximately cast the sender's problem into alinearly-constrained mathematical program whose objective function is themulti-linear extension of the sender's utility. Then, we show how to find inpolynomial-time an approximate solution to the program by means of a continuousgreedy algorithm. This provides a (1 -1/e)-approximation to the problem.

Bayesian Persuasion Meets Mechanism Design: Going Beyond Intractability with Type Reporting