Public Signaling in Bayesian Ad Auctions

Bacchiocchi, Francesco; Castiglioni, Matteo; Marchesi, Alberto; Romano, Giulia; Gatti, Nicola

doi:10.48550/arxiv.2201.09728

Cited by 1 publication

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“…In particular, it defines how the sender should send private signals to the receivers, essentially deciding "who gets to know what". These kinds of problems are ubiquitous in applications such as auctions and online advertising [5,6,8,17,23], voting [1,11,12,15,18], traffic routing [7,14,30], recommendation systems [27], security [28,33], and product marketing [3,10].…”

Section: Introductionmentioning

confidence: 99%

“…Update to make it consistent with the menus of marginal signaling schemes { , } ∈R 14: return we relaxed Constraints (8b), the feasible region is a down-monotone polytope 5 and it is defined by polynomially-many constraints. For each > 0, this problem admits a 1 − 1 − -approximation in time polynomial in the instance size and , see the continuous greedy algorithm in [9] and [22] for a formulation in a similar problem.…”

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confidence: 99%

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

Castiglioni¹,

Marchesi²,

Gatti³

2022

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Bayesian persuasion studies how an informed sender should partially disclose information so as to influence the behavior of selfinterested receivers. In the last years, a growing attention has been devoted to relaxing the assumption that the sender perfectly knows receiver's payoffs. The first crucial step towards such an achievement is to study settings where each receiver's payoffs depend on their unknown type, which is randomly determined by a known finite-supported probability distribution. This begets considerable computational challenges, as computing a sender-optimal signaling scheme is inapproximable up to within any constant factor, even in basic settings with a single receiver. In this work, we circumvent this issue by leveraging ideas from mechanism design. In particular, we introduce a type reporting step in which the receiver is asked to report their type to the sender, after the latter has committed to a menu defining a signaling scheme for each possible receiver's type. Surprisingly, we prove that, with a single receiver, the addition of this type reporting stage makes the sender's computational problem tractable. Then, we extend our Bayesian persuasion framework with type reporting to settings with multiple receivers, focusing on the widely-studied case of no interagent externalities and binary actions. In such setting, we show that it is possible to find a sender-optimal solution in polynomialtime by means of the ellipsoid method, given access to a suitable polynomial-time separation oracle. This can be implemented for supermodular and anonymous sender's utility functions. As for the case of submodular sender's utility functions, we first approximately cast the sender's problem into a linearly-constrained mathematical program whose objective function is the multi-linear extension of the sender's utility. Then, we show how to find in polynomialtime an approximate solution to the program by means of a continuous greedy algorithm. This provides a 1 − 1 -approximation to the problem, which is tight.

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