Dynamic information disclosure

• Date: 01 October 2015
• DOI: http://doi.org/10.1111/1756-2171.12111
• Published date: 01 October 2015
• Author: Pak Hung Au

RAND Journal of Economics

Vol.46, No. 4, Winter 2015

pp. 791–823

Dynamic information disclosure

Pak Hung Au∗

Westudy dynamic information disclosure by a sender attempting to persuade a partially informed

receiver to take an action. We consider vertical and horizontal information. With vertical infor-

mation, an optimal disclosure plan is static. If the sender cannot commit to the disclosure plan,

there exists a simple Markov equilibrium with sequential disclosure. Shrinking the time interval

to zero gives rise to full disclosurealmost instantly. With horizontal information, the sender often

benefits from sequential disclosure. Assuming partial commitment and a special receiver-type

space, a Markov equilibrium exists and almost instant full disclosurearises in the limit.

1. Introduction

This article studies information revelation by a sender who wants to persuade a partially

informed receiver to take an action. There are many examples of this type of interaction int hereal

world. Consider the drug approvalprocess by the Food and Drug Administration (FDA).1Suppose

a pharmaceutical company seeks FDA approval to market a new drug. It submits an application

to the FDA with a detailed protocol for clinical testings of the drug. Throughout the testing stage,

the FDA closely monitors the implementation to ensure adherence to safety standards and the

testing plan. After getting the test results, the FDA conducts an independent review and makesits

recommendations. If the application is rejected, the pharmaceutical company can reapply with a

new protocol of additional tests and studies. The application process can take multiple rounds.2

Suppose a salesperson (e.g., a used-car dealer or a real estate agent) wants to persuade a

customer to purchase a product. The product has some attributes unknown to the customer,and the

salesperson can choose when and how to revealthe product’s attribute information. The customer

privately knows his preference and makesa purchase provided the product’s characteristics are a

∗Nanyang TechnologicalUniversity; phau@ntu.edu.sg.

This article is a revised version of a chapter from my dissertation at Northwestern University. I am greatly indebted to

my advisors, Asher Wolinsky, Yuk-Fai Fong, and Jin Li for their continuous guidance, encouragement, and invaluable

advice. A lot of thanks to the Editor and two anonymous referees whose comments and suggestions have substantially

improvedthe ar ticle. I am also grateful for the helpful discussion with JimmyChan, Keiichi Kawai, and participants at the

2012 Workshop in Industrial Organization and Management Strategy, 2013 Australasian Economic Theory Workshop,

the 2013 Asian Meeting of the Econometric Society, and the 2013 Singapore Economic Review Conference. Financial

support by the Dissertation YearFellowship of Northwestern University, and the startup grant of Shanghai Universityof

Finance and Economics, are gratefully acknowledged. All errors are my own.

1For a detailed description of the process, see Lipsky and Sharp (2001).

2Recent examples of drugs being rejected in the first application and approved in the second application are the

weight-loss drugs Belviq and Qsymia.

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sufficiently good match with his preference. Similar persuasion problems are faced byadvertising

agencies designing a marketing campaign (what details to include in a sequence of ads), and

software producers designing the free-trial versions of their products (what features to include in

a sequence of trial versions).

Weare interested in the sender’s strategy concerning dynamic information disclosure. When

does sequential disclosure benefit the sender? Does it arise in equilibrium? If it does, what form

does it take? To study these questions, we consider the following dynamic sender-receiver game.

In each period, the receiver can take an irreversible action, the payoff of which depends on an

unknown state of the world, as well as his private type. Only when the receiver takes the action

does the sender receive a positive state-independent payoff. Both players share the same discount

factor. The sender designs a sequence of mechanisms that (partially or fully) informs the receiver

of the state. The choice of disclosure mechanism and the receiver’s action are not contractible.

The receiver forms his belief about the payoff of taking the action based on his private type and

the information revealed by the sender’s mechanism. The receiver’s objective is to maximize his

expected payoff,taking into account the anticipated disclosure mechanisms in the future. Once the

receiver takes the action, the game is over. Otherwise, the game proceeds to the next period, with

the sender offering another disclosure mechanism. A sequence of disclosure mechanism is called

an information policy. Westudy the case in which the sender can commit to the information policy

at the very beginning of the game, and the case in which she can only commit to the mechanism

in the current period. Most of our analysis assumes that the sender does not observe the state of

the world when designing her information policy. We show that some results can be carried over

to the alternative setting in which the sender knows the state of the world.

We distinguish our analysis according to how the receiver’s action payoff depends on the

state of the world and his private type. In the case of vertical information, a higher state and

receiver’s type are more favorable for taking the action. If the FDA’s concern is primarily about

the overall quality of the drug, then a good quality of the drug (high state) and a favorable result

of independent review (high type) both support approval. In the case of horizontal information,

whether a state is more favorable for action depends on the receiver’s type. The salesperson

example fits this case, as the buyer’s utility in consuming the goods depends on whether its

attribute (the state) matches with his preference (the type).3

At first glance, sequential information disclosure may benefit the sender because it helps

screen the receiver’s type. Consider the vertical information case. A high-type receiver, being

optimistic about its payoff, prefers taking the action immediately without suffering the cost of

delay, even if the information provided by the sender is not strongly favorable. By contrast, a

low-type receiver, being pessimisticabout the payoff of taking the action, must be provided with

strongly favorable information before he is persuaded to act. By disclosing a small amount of

information in the early stages, the sender can induce the action from an optimistic receiver

with a high probability. In later stages, a pessimistic receiver may be induced to act as further

information is disclosed. In other words, the sender can engage in “intertemporal information

discrimination.”

On the other hand, there are costs associated with sequential disclosure. Anticipating that

further information will arrive soon, a receiver is inclined to wait and see, even if the initial

information is already favorable for action. As the receiver becomes more demanding, the chance

of successful persuasion decreases. We find that this benefit-cost comparison depends crucially

on the nature of the information being disclosed.

3The drug approval process may also involvesome component of horizontal information. Suppose there is uncer-

tainty regarding the FDA’s relative concern for the drug’ssafety versus its efficacy. This can be modelled as two receiver

types: (i) weighs safety more or (ii) weighs efficacy more. Suppose two possible states are (a) the drug is safe but not

effective or (b) the drug is effectivebut has strong side effects. A receiver of type (i) would be happy to take action were

the state known to be (a), but not (b). Conversely, a receiver of type (ii) would be happy to take action were the state

known to be (b), but not (a).

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Our first result is that in the vertical information case, the sender does not benefit from

sequential disclosure. More precisely, when the sender has full commitment power, one of the

optimal information policies is static: it discloses no further information beyond the first period.

Depending on the distribution of the receiver’s type and his payoff function of action, the sender’s

optimal mechanism can either be no disclosure, partial disclosure, or full disclosure.4

There are natural situations in which the sender cannot commit to future disclosure. If some

types of the receiver demand an almost certain knowledge about the state to be persuaded, then

the sender is tempted to reveal further information whenever the initial information is positive

but fails to persuade the receiver to act. Therefore, whenever the optimal information policy

does not offer full disclosure in the first period, it is not sequentially rational for the sender. We

consider a setting in which the sender can commit only to the disclosure mechanism chosen in

the current period and focus on the monotone Markov equilibrium of such a disclosure game. In a

monotone Markov equilibrium, each receiver uses a cutoffstrategy: he takes the action whenever

the posterior belief about the state of the world exceeds a type-dependent threshold. The sender’s

offer of disclosure mechanism depends only on the posterior belief and the set of remaining

receiver types. We show that a monotone Markov equilibrium exists and is essentially unique. In

the equilibrium, the sender reveals increasingly precise information about the state of the world

over time, and ends the game with full disclosure in finite time. Furthermore, we are interested

in the equilibrium outcome as the sender’s commitment ability vanishes, a scenario modelled by

shrinking the length of the time period to zero. It is found that the sender fully discloses the state

of the world “in the blink of an eye” a Coase-conjecture result for information disclosure.

Contrary to the vertical information case, in disclosing horizontal information under full

commitment, we find that the sender can often benefit from disclosing gradually over time.

The difference in results is due to the lower cost involved in sequential disclosure of horizontal

information. With a binary receiver-type space, weare able to explicitly solve the optimal dynamic

information policy. Using this result, we offer sufficient conditions for the strict optimality of

sequential disclosure with a continuous receiver-type space. We then consider an alternative

setting in which the sender knows the state of the worldfrom the outset. This tur ns the model into

one of signalling, as the receiver can make inferences from the sender’s choice of information

policy given her equilibrium strategy. We identify a simple sufficient condition for the existence

of a pooling equilibrium in which the sender alwaysoffers the ex ante optimal information policy.

Whenever it exists, this pooling equilibrium is plausible as it satisfies a versionof Cho and Kreps’

(1987) Intuitive Criterion adapted to the current setting,5and it gives the highest ex ante payoff

to the sender among all signalling equilibria.

Finally, we study disclosing horizontal information under partial commitment. The problem

is technically challenging. Tomake progress, we focus on a special binary type space in which one

type of receiver needs to be certain of the state to be persuaded. A monotone Markov equilibrium

can be explicitly constructed and shown to be essentially unique. Moreover, the Coase-conjecture

result of instantaneous full disclosure holds in the limit as the length of the time period shrinks

to zero.

The strategic behavior considered here suggests that if the sender cannot commit to her

information policy, then she discloses more information and does so more quickly compared

to the case in which she can fully commit. As the receiver always benefits (weakly) from more

information, it can be in his interest to provide more opportunities for the sender to revise her

information policy and disclose further information. For instance, the FDA may end up better

4Intuitively, no disclosure can be optimal if the receiver is likely to have a high type, so with high probability,

action is taken immediately even in the absence of further information about the state of the world. On the other hand,

full disclosure can be optimal if the receiver is likely to havea low type.

5The Intuitive Criterion is modified to (i) allow for the possibility that different types of receivershold different

off-the-equilibrium-path beliefs, as well as (ii) ensure that the receiver can always be persuaded by a sufficiently strong

verifiable signal sent by the disclosure mechanisms.

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The RAND Corporation 2015.