Optimal monotone signals in Bayesian persuasion mechanisms

Ivanov, Maxim

doi:10.1007/s00199-020-01277-x

Cited by 21 publications

(13 citation statements)

References 28 publications

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“…Combined with Theorem 1, Lemma 1 implies that when the Sender's preference is strictly supermodular, the credibility of a profile (λ, σ) is equivalent to the comonotonicity of its induced outcome distribution. Comonotone outcome distributions have attracted much attention in the persuasion literature in part due to their simplicity and ease of implementation; for example, see Dworczak and Martini (2019), Goldstein and Leitner (2018), Mensch (2021), Ivanov (2020), Kolotilin (2018), and Kolotilin and Li (2020). Our credibility notion provides an additional motive for focusing on monotone information structures.…”

Section: Modular Preferencesmentioning

confidence: 99%

Credible Persuasion

Lin¹,

Liu²

2022

Preprint

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We propose a new notion of credibility for Bayesian persuasion problems. A disclosure policy is credible if the sender cannot profit from tampering with her messages while keeping the message distribution unchanged. We show that the credibility of a disclosure policy is equivalent to a cyclical monotonicity condition on its induced distribution over states and actions. We also characterize how credibility restricts the Sender's ability to persuade under different payoff structures. In particular, when the sender's payoff is state-independent, all disclosure policies are credible. We apply our results to the market for lemons, and show that no useful information can be credibly disclosed by the seller, even though a seller who can commit to her disclosure policy would perfectly reveal her private information to maximize profit. * We are indebted to Nageeb Ali for his continuing guidance and support. We are also grateful for comments and suggestions from

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Section: Modular Preferencesmentioning

confidence: 99%

Credible Persuasion

Lin¹,

Liu²

2022

Preprint

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“…. This structure is important in optimal information provision for continuous parameters as these intervalbased signalling mechanisms correspond to the vertices of the polytope containing all feasible signalling mechanisms over the parameter [12,14,20,25]. Each instance of our game for a particular initial mass vector x and public belief G over Θ can be expressed in normal form Γ(x,…”

Section: Signalling and Central Planner Objectivementioning

confidence: 99%

“…We implement an experiment where Y = {y : y ≥ b} and we vary the constants b between 0 and 1 in increments of 1 20 . The number of groups is fixed at K = 10 and for each b we run 10, 000 simulations by drawing x ∼ U nif (L 1 ), v i ∼ U nif [0, 10], θ ∼ U nif [5,20] (µ = 25 2 ). We evaluate the optimal mechanism given by Theorem 3.1 against two benchmarks.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Optimal Information Provision for Strategic Hybrid Workers

Shah¹,

Amin²,

Jaillet³

2022

Preprint

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We study the problem of information provision by a strategic central planner who can publicly signal about an uncertain infectious risk parameter. Signalling leads to an updated public belief over the parameter, and agents then make equilibrium choices on whether to work remotely or in-person. The planner maintains a set of desirable outcomes for each realization of the uncertain parameter and seeks to maximize the probability that agents choose an acceptable outcome for the true parameter. We distinguish between stateless and stateful objectives. In the former, the set of desirable outcomes does not change as a function of the risk parameter, whereas in the latter it does. For stateless objectives, we reduce the problem to maximizing the probability of inducing mean beliefs that lie in intervals computable from the set of desirable outcomes. We derive the optimal signalling mechanism and show that it partitions the parameter domain into at most two intervals with the signals generated according to an interval-specific distribution. For the stateful case, we consider a practically relevant situation in which the planner can enforce in-person work capacity limits that progressively get more stringent as the risk parameter increases. We show that the optimal signalling mechanism for this case can be obtained by solving a linear program. We numerically verify the improvement in achieving desirable outcomes using our information design relative to no information and full information benchmarks.

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“…Assumption 1 is natural in many economic situations and is commonly made in the literature (e.g., Ostrovsky and Schwarz 2010;Ivanov 2015;Gentzkow and Kamenica 2016b;Kolotilin 2018;Dworczak and Martini 2019). 11 For example Kolotilin et al (2017) assume that there are two actions A = {0, 1} and that the receiver's utility for one action is zero, and for the other action it is the sum of the type and state, which implies that u(a, ω, θ) = a × (ω + θ).…”

Section: Signals and Mechanismsmentioning

confidence: 99%

Optimal Disclosure of Information to a Privately Informed Receiver

Candogan

Strack

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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We study information design problems where the designer controls information about a state and the receiver is privately informed about his preferences. The receiver's action set is general and his preferences depend linearly on the state. We show that to optimally screen the receiver, the designer can use a menu of "laminar partitional" signals. These signals partition the states such that the same message is sent in each partition element and the convex hulls of any two partition elements are either nested or have an empty intersection. Furthermore, each state is either perfectly revealed or lies in an interval in which at most n + 2 different messages are sent, where n is the number of receiver types. In the finite action case an optimal menu can be obtained by solving a finite-dimensional convex program. Along the way we shed light on the solutions of optimization problems over distributions subject to a mean-preserving contraction constraint and additional constraints which might be of independent interest.

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Optimal monotone signals in Bayesian persuasion mechanisms

Cited by 21 publications

References 28 publications

Credible Persuasion

Credible Persuasion

Optimal Information Provision for Strategic Hybrid Workers

Optimal Disclosure of Information to a Privately Informed Receiver

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