The Simple Economics of Optimal Persuasion

Dworczak, Piotr; Martini, Giorgio

doi:10.1086/701813

Cited by 171 publications

(154 citation statements)

References 15 publications

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“…Calculating the concave envelope over the (infinite‐dimensional) space of distributions is typically difficult, and most papers that derive an explicit solution to Sender's problem require V to be a function of the posterior expectation

\int s γ false(normald s false)

alone (see Gentzkow and Kamenica (), Dworczak and Martini (), and Kolotilin et al ()). Our Example is beyond the scope of these papers.…”

Section: The Binary‐type Casementioning

confidence: 99%

The Interval Structure of Optimal Disclosure

Guo¹,

Shmaya

2019

ECTA

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A sender persuades a receiver to accept a project by disclosing information about a payoff‐relevant quality. The receiver has private information about the quality, referred to as his type. We show that the sender‐optimal mechanism takes the form of nested intervals: each type accepts on an interval of qualities and a more optimistic type's interval contains a less optimistic type's interval. This nested‐interval structure offers a simple algorithm to solve for the optimal disclosure and connects our problem to the monopoly screening problem. The mechanism is optimal even if the sender conditions the disclosure mechanism on the receiver's reported type.

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\int s γ false(normald s false)

alone (see Gentzkow and Kamenica (), Dworczak and Martini (), and Kolotilin et al ()). Our Example is beyond the scope of these papers.…”

Section: The Binary‐type Casementioning

confidence: 99%

The Interval Structure of Optimal Disclosure

Guo¹,

Shmaya

2019

ECTA

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“…We now consider the implications of adding disappointment aversion to a problem of Bayesian persuasion. We focus on the special case studied in Dworczak and Martini (2019, Section VI.A). A sender and a receiver share a full‐support prior r with continuous cumulative distribution function and expectation

\overset{μ}{true}

on a state of the world

x \in false[0, 1 false]

.…”

Section: Optimization and Applicationsmentioning

confidence: 99%

“…The receiver chooses action

e \in false[0, ē false]

, where

ē \leq 1

. Following Dworczak and Martini (2019), we focus on the case in which both the sender's and receiver's utility,

u_{normalS}

and

u_{normalR}

, respectively, depend only on the receiver's posterior mean y and action e :

u_{normalS} false(e, y false) = false(1 - σ false) e y u_{normalR} false(y, e false) = σ y e - e^{α}, where 0 < σ < 1 and α > 1 .

In equilibrium, the sender's utility can be rewritten as

u false(y false) = false(1 - σ false) e^{*} false(y false) y \forall y \in false[0, 1 false],

where

e^{*} false(y false)

is the receiver's optimal action 9 . As is standard in this literature, the sender's problem amounts to choosing a distribution over the receiver's posteriors, and since here only their means matter, this simplifies to choosing a distribution over posterior means.…”

Section: Optimization and Applicationsmentioning

confidence: 99%

An explicit representation for disappointment aversion and other betweenness preferences

Cerreia‐Vioglio

Dillenberger

Ortoleva

2020

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One of the most well known models of non‐expected utility is Gul's (1991) model of disappointment aversion. This model, however, is defined implicitly, as the solution to a functional equation; its explicit utility representation is unknown, which may limit its applicability. We show that an explicit representation can be easily constructed, using solely the components of the implicit representation. We also provide a more general result: an explicit representation for preferences in the betweenness class that also satisfy negative certainty independence (Dillenberger 2010) or its counterpart. We show how our approach gives a simple way to identify the parameters of the representation behaviorally and to study the consequences of disappointment aversion in a variety of applications.

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“…Lemma 5 In equilibrium, a bank of type agrees to sell at price x if and only if x ( ). 17 An example of a probability distribution function that satis…es the condition above is a truncated Cauchy distribution (Nadarajah and Kotz, 2006) on the interval [ A; 0] minus its mean, where the lower bound A depends on the model parameters. Intuitively, for the su¢ cient condition above to hold, we must have F (1…”

Section: Derivation Of the Regulator' S Problemmentioning

confidence: 99%

Stress Tests and Information Disclosure

Goldstein

Leitner

2018

Working Paper (Federal Reserve Bank of Philadelphia)

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We study an optimal disclosure policy of a regulator that has information about banks (e.g., from conducting stress tests). In our model, disclosure can destroy risk-sharing opportunities for banks (the Hirshleifer e¤ect). Yet, in some cases, some level of disclosure is necessary for risk sharing to occur. We provide conditions under which optimal disclosure takes a simple form (e.g., full disclosure, no disclosure, or a cuto¤ rule). We also show that, in some cases, optimal disclosure takes a more complicated form (e.g., multiple cuto¤s or nonmonotone rules), which we characterize. We relate our results to the Bayesian persuasion literature.

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The Simple Economics of Optimal Persuasion

Cited by 171 publications

References 15 publications

The Interval Structure of Optimal Disclosure

The Interval Structure of Optimal Disclosure

An explicit representation for disappointment aversion and other betweenness preferences

Stress Tests and Information Disclosure

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