BAYESIAN PERSUASION WITH PRIVATE EXPERIMENTATION

• Date: 01 August 2017
• DOI: http://doi.org/10.1111/iere.12237
• Published date: 01 August 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

BAYESIAN PERSUASION WITH PRIVATE EXPERIMENTATION∗

BYMIKE FELGENHAUER AND PETRA LOERKE1

Plymouth University, U.K.; NERA Economic Consulting, Germany

This article studies a situation in which a sender tries to persuade a receiver by providing hard evidence

that is generated by sequential private experimentation where the sender can design the properties of each

experiment contingent on the experimentation history. The sender can selectively reveal as many outcomes as

desired. We determine the set of equilibria that are not Pareto-dominated. In each of these equilibria under

private experimentation, the persuasion probability is lower and the receiver obtains access to higher quality

information than under public experimentation. The decision quality improves in the sender’s stakes.

1. INTRODUCTION

There are many situations in which arguments are exchanged, as in lobbying, public discus-

sions of economic policies, the academic publishing process, etc. Arguments have an inherent

meaning and are not cheap talk. We think that many arguments, like logical arguments or

a regression analysis on a public database, can be viewed as hard (i.e., nonmanipulable) and

imperfect decision-relevant evidence.2Furthermore, arguments often have to be acquired.

Kamenica and Gentzkow (2011) describe a trial as a public experiment yielding an argument.

The prosecutor can design the error probabilities in order to achieve his objectives. The error

probabilities can be affected, e.g., by structuring the examination of witnesses in court. They

determine the prosecutor’s optimal experiment for persuading a Bayesian judge.

Although a public experiment is an interesting case for generating an argument, there is

an abundance of situations in which arguments stem from sequential private experimentation.

For example, if a sender wants to persuade a receiver with logical arguments, then he runs a

series of thought experiments.3He privately chooses the properties of each experiment, e.g.,

by choosing the conceptual framework from which to draw a set of specific assumptions. The

outcome of each thought experiment is privately observed. Naturally, he may run as many

thought experiments with properties of his choice (depending on what he has learned from

∗Manuscript received June 2015; revised April 2016.

1An early version of this article circulated under the title “Public versus Private Experimentation.” We thank

Johannes H¨

orner, Andras Niedermayer, Elisabeth Schulte, Nicolas Schutz, Dmitry Shapiro, Ran Spiegler, Roland

Strausz, Ernst-Ludwig von Thadden, and Juuso V¨

alim¨

aki for valuable comments and suggestions. A substantial part

of the work on this article was done while the authors were at the University of Mannheim. Their support is gratefully

acknowledged. The opinions expressed in this article are those of the authors and should not be regarded as those of

NERA Economic Consulting.

Please address correspondence to: Mike Felgenhauer, Plymouth University, Cookworthy Building, Plymouth PL4

8AA, U.K. Phone: 01752-585541. E-mail: mike.felgenhauer@plymouth.ac.uk.

2Once a regression method is described and the database is public, manipulation is not possible. We make a similar

case for logical arguments in footnote 3. Such arguments have persuasive power, and, hence, they can be viewed as

decision relevant. Naturally, they are also imperfect.

3Felgenhauer and Schulte (2014) interpret, e.g., logical arguments as decision relevant hard information that result

from experimentation: If the assumptions underlying a logical argument are revealed, then they cannot be manipulated.

The deductions are logical and logic cannot be manipulated. Logical arguments have persuasive power; therefore, they

can be viewed as signals about a decision relevant state of the world. The signals are imperfect, as the underlying

assumptions do not cover every real world aspect. A thought experiment (i.e., drawing a set of assumptions and making

a deduction) yields a signal. For such arguments the assumption that they are acquired in private by running a series of

thought experiments and selectively revealed for persuasion is natural.

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

830 FELGENHAUER AND LOERKE

previous experimentation) as desired and selectively reveal the results. If a sender instead

wants to persuade with an empirical analysis using a public database, then he may run a series

of regressions. By choosing the econometric method and the model specification, he chooses the

properties of each experiment. Again, experimentation is sequential, and the privately observed

results are revealed selectively.

This article studies a situation in which a sender tries to persuade a Bayesian receiver by

providing experimental evidence that stems from sequential experimentation. Information ac-

quisition occurs in private, and the experimental evidence can be selectively revealed. We

assume that an experimental outcome is hard evidence, that the sender designs the precision of

each experiment contingent on the experimentation history, and that his decision to continue

experimenting also depends on the experimentation history.

If arguments stem from sequential private experimentation and are selectively revealed, then

the revealed evidence should not be taken at face value. The value of such arguments depends

on the equilibrium experimentation plan, which, in turn, is influenced by experimentation costs

and the sender’s benefit from the receiver’s decision. An experimentation plan in our model is

a complex object, since the sender can make many history dependent choices. The sender also

has considerable degrees of freedom regarding the messages that he can send, as he may reveal

any subset of the acquired evidence, including “counterarguments.”

We derive the set of equilibria that are not Pareto-dominated under private experimentation

for constant experimentation costs. In each of these equilibria, the sender runs one experiment

and stops after observing either realization. In the sender-preferred equilibrium, the precision

of the experiment is sufficiently high such that the sender is just deterred from continuing

experimentation after observing an adverse outcome. In any other equilibrium that is not Pareto-

dominated, the precision is even higher. The persuasion probability in any such equilibrium is

lower than under public experimentation. Private experimentation thus limits the extent to

which persuasion is possible.

We compare the payoffs under public and private experimentation. Under private experimen-

tation, the sender is worse off than under public experimentation due to the lower persuasion

probability. The receiver, on the other hand, is better off in each of these equilibria under

private experimentation due to the higher precision of the experiment.

As an application consider a pharmaceutical company (the sender) that attempts to persuade

the U.S. Food and Drug Administration (the receiver) to approve a newly developed drug.

Given the enormous research & development (R&D) costs in the pharmaceutical industry, it is

plausible that the company prefers that a new drug be approved, even if its merits are doubtful.

The FDA instead would like to make the “appropriate” decision, which could be against the

company. The FDA mainly has to rely on tests, e.g., clinical studies, provided by the company,

which, in turn, has an incentive to behave strategically. The decision quality can be influenced

by the rules under which evidence can be acquired and revealed and what evidence is permitted

to be considered as decision relevant. The evidence production may be designed as public, by

imposing severe penalties if this rule is violated, or as private. Our article suggests that the FDA

would be better off under the private scheme, but the company would benefit more from public

experimentation.

We analyze the impact of the sender’s stakes on the decision quality. We compare a situ-

ation where a sender does not care much about his favored decision with a situation where

he cares substantially. We find that the decision quality in any equilibrium that is not Pareto-

dominated in the former case is lower than in any equilibrium that is not Pareto-dominated

in the latter case. In a context where an interested party (like a lobby, student, researcher,

etc.) tries to persuade a decision maker (like a politician, teacher, editor, etc.) to choose

a favorable action (like a policy, a better mark in the exam, the publication of a paper,

etc.), this means that the decision maker is better off the more the interested party benefits

from a favorable decision. The interested party then has to provide higher quality informa-

tion in order to be able to commit not to run additional private experiments after an initial

failure.