Giving and Receiving Advice
∗
Joel Sobel
†
May 5, 2011
Abstract
This paper reviews literature on communication between informed
experts and uninformed decision makers. The research provides some
insight into what constitutes a persuasive statement and under what
conditions a decision maker will benefit from consulting an expert. I
classify the literature along four dimensions: strategic, technological,
institutional, and cultural. To the extent that decision makers and
experts have different preferences, communication creates strategic
problems. Technological considerations describe the domain of uncer-
tainty, the cost of acquiring information, and the cost of manipulating
information. The institution determines who has responsibility for
making decisions and the rules that govern communication. Cultural
factors describe the way in which agents interpret language.
Keywords: communication, signaling.
JEL Classification Numbers: D02, D03, D44.
∗
I thank Nageeb Ali, Marco Battaglini, Andreas Blume, Antonio Cabrales, Ying Chen,
Vincent Crawford, Stefano Demichelis, Wouter Dessein, Eddie Dekel, Navin Kartik, Kohei
Kawamura, Chulyoung Kim, Young-Gwan Kim, Fr´ed´eric Koessler, David Miller, Roger
Myerson, Philip Neary, Lucas Siga, Ran Spiegler, Joel Watson, and Kathryn Woolard for
encouragement and wisdom. I am grateful to the NSF for financial support.
†
Department of Economics, University of California, San Diego, La Jolla, CA 92093,
U.S.A. E-mail: jsobel@ucsd.edu
1 Introduction
Models of signaling, adverse selection, and moral hazard make it clear that
differences in information can lead to inefficiency. Workers may invest in
non-productive education in order to convince an employer they have skills.
Markets may fail when sellers know more about the quality of their item
than buyers. Risk-neutral principals may fail to offer perfect insurance to
risk-averse workers when they cannot directly observe the workers’ choice of
effort.
If asymmetric information leads to inefficiency, why can’t agents improve
outcomes by direct, costless communication? This question motivates the
study of cheap-talk models. It has a straightforward answer. In simple
economic environments it is not in the interest of one agent to reveal private
information to another. Naive and honest sellers who accurately reveal the
quality of their item may lose all bargaining power. Credulous employers
who believe a worker’s claims about productivity encourage workers to make
exaggerated claims about their quality. Adding realistic complications to
these situations creates situations in which this kind of cheap talk can be
beneficial.
In this essay, I discuss some concepts central to the study of commu-
nication. I illustrate most of the ideas using a model in which there is an
informed agent who has the ability to communicate with an uninformed de-
cision maker. The informed Sender gives advice. The uninformed Receiver
decides how to use it. The fundamental questions in this environment are:
How credible can communication be? What factors lead to no communica-
tion? What conditions are consistent with full communication? How does
one organize environments so that communication is most effective?
The next section outlines models in which one can formulate these ques-
tions. Section 3 describes how the differences in preferences between the
Sender and Receiver may limit the ability to communicate. The Sender may
have strategic reasons for distorting information and the Receiver may have
strategic reasons to be skeptical. The theory formalizes the intuition that
communication is more successful if the interests of the parties are more
closely aligned.
Interesting communication problems must be associated with multiple
equilibria. In Section 4, I argue that non-trivial communication can be guar-
anteed only if players use exogenous factors that induce common understand-
ing of messages. Theory does not permit the modeler to make precise pre-
1
dictions without making assumptions about how agents interpret language.
The cultural context of interaction may place restrictions on the relation-
ship between the Sender’s private information and the messages she uses to
describe it.
Section 5 studies the communication problem when there are many in-
formed agents. Adding additional sources of information typically increases
the opportunities for information exchange in standard models even when
the informed agents have access to identical information.
In a simple environment with a single informed agent and a single deci-
sion maker, direct one-shot communication is one of many ways to structure
the communication problem. To gain an insight into how best to communi-
cate, it is essential to look at the problem of institution design. Section 6
examines models that give some actor commitment power and describes how
to structure communication to benefit the uninformed agent.
Section 7 looks at the institution design problem from the perspective of
the informed agent. When the Sender has commitment power, the Receiver
can be more credulous as the Sender can convincingly promise not to distort
her information when it is in her strategic interest to do so. Section 8 shows
that related results are possible when information is verifiable so that what
the Sender can say is constrained by what the Sender knows.
Section 9 points out some connections between economic models of com-
munication and linguistics.
Section 10 and 11 discuss two significant variations on the basic model
that call attention to assumptions on the communication technology. Sec-
tion 10 relaxes the assumption that information is exogenously given. The
actors have different opinions not only about the final decision, but about
how much to invest in collecting information. There is typically a tension
between factors that provide incentives to gather information and those that
provide incentive to communicate the information accurately.
Section 11 points out that the limiting factor in communication may not
be incentive problems, but the complexity of information itself. It describes
some issues that arise when information is costly to prepare and costly to
interpret.
Section 12 is a conclusion.
2
2 Framework
I use a simple model to describe communication. The essential features are
two agents, an informed Sender (S) and an uninformed Receiver (R). These
agents have preferences that depend on an action a ∈ A and a state of
the world θ ∈ Θ. Denote these preferences by U
i
(·) for i = R, S. Nature
selects θ according to a common-knowledge distribution, p(·). For most of
the discussion, I assume that the Sender learns θ without cost.
Starting from these basic assumptions, there are several possible ways
to complete the description of the strategic interaction. I introduce some
variations in this section. In a cheap-talk game (Crawford and Sobel [21]
and Green and Stokey [41]) there is an abstract set of messages M, a set of
states (or types) Θ, and a set of actions, A. S learns θ, selects a message
m ∈ M and R selects an action a ∈ A. Formally, a (mixed) strategy for the
Receiver is denoted by α, where α(a | m) is the probability that the Receiver
takes action a ∈ A given message m ∈ M. A (mixed) strategy for the Sender
is denoted by σ, where σ(m | θ) is the probability that the Sender sends
message m when her type is θ ∈ Θ. An equilibrium consists of a strategy
profile (α
∗
, σ
∗
) and a belief function µ
∗
(µ
∗
(θ | m) is the probability that the
Receiver believes that the Sender’s type is θ given message m), such that α
∗
is a best response to µ
∗
; σ
∗
is a best response to α
∗
; and µ
∗
is consistent
with the prior and σ
∗
in the sense that Bayes’s Rule determines µ
∗
(· | m) for
all m such that
P
θ∈Θ
p(θ)σ
∗
(m | θ) > 0.
1
I will discuss cheap-talk models
in more detail in Section 3 and Section 4. Section 5 discusses models with
many Senders.
In cheap-talk games, the set of messages available to the Sender does
not depend on the state of the world. Disclosure games arise when what
the Sender knows constrains what the Sender can say. Grossman [43] and
Milgrom [66] introduce models of hard, or verifiable, information. When
information is verifiable, the set of messages M is the set of all subsets of Θ
and S’s strategies are constrained so that the Sender of type θ can only use
a message m if θ ∈ m. That is, the Sender can withhold information, but
cannot misrepresent information. I discuss these ideas in Section 8.
The basic model of cheap talk assumes that players lack the ability to
make commitments. To answer the question of how to design organizations
1
Jung [51] comments on the appropriate definition of equilibrium when strategy spaces
are large.
3
to improve communication, it is important to consider the possibility that
one or the other agent has the ability to commit to a strategy or that the
players can use a third party to facilitate the interaction. Section 6 and
Section 7 discuss environments in which one player has commitment power.
This paper neglects many topics including career concern or dynamics,
monetary transfers, and privately informed Receivers.
3 Strategic Considerations
If the Receiver has a best response to the prior distribution (an assump-
tion that I maintain throughout this essay), then cheap-talk games have a
“babbling” equilibrium in which there is no communication. Assume that
the uninformed agent takes the same action independent of the signal (this
action should be a best response to the prior). In this case all Sender types
are indifferent between all signals. In particular, it is a best response for
all of them to say the same thing.
2
This equilibrium outcome is similar to
the pooling outcome of classical signaling models. In labor-market signal-
ing, however, the response to out-of-equilibrium messages typically must be
different than the response to the message used on the path of the pooling
equilibrium (in particular, if there is pooling at a positive level of education,
then the response to “no education” must be a lower salary than the equilib-
rium salary, otherwise no one would get education). In cheap-talk games all
responses can be the same (and, in some examples, they must be the same)
as the response on the equilibrium path.
The observation that cheap-talk games always have babbling equilibria
motivates two important questions one can ask about communication games.
Under what conditions is babbling the only equilibrium outcome? Under
what conditions is there a fully revealing equilibrium?
When the only equilibria involve babbling, the opportunity to communi-
cate freely does not enlarge the set of predictions. In this case, cheap talk
cannot ameliorate problems caused by asymmetries in information. When
2
One can always take a game and form a new game in which players can engage in
costless pre-play communication. When the underlying game has an equilibrium, the
augmented game will have a babbling equilibrium in which all messages are ignored. Seid-
man [75] provides an example of a game with pre-play communication that has a unique
informative equilibrium outcome but no babbling equilibrium. This is possible because
the game without communication does not have an equilibrium.
4