erosion of meaning - an experimentcepr.org/sites/default/files/6721_blume - erosion of...
TRANSCRIPT
Erosion of meaning - an experiment
Andreas Blume∗ Charles N. Noussair† Bohan Ye‡
May 16, 2017
Abstract
The experiment reported in this paper investigates communication between a sender and areceiver who have a language that is only imperfectly shared between them. The players agreeon the best action conditional on the payoff state. Incomplete information about language,however, leads to incentive problems. Senders who lack the messages to describe the true payoffstate have an incentive to indicate other payoff states that they are able to describe. Our centralbehavioral hypothesis is that initially experimental subjects will use messages consistent withtheir focal meaning, but behavior will eventually gravitate to a pooling equilibrium, in whichmessages are not believed and outcomes are inefficient. We refer to this dynamic process as anErosion of Meaning. The experimental results support our central hypothesis. Receivers learnto ignore the messages they receive, and choose a pooling action that delivers a safe payoff. Thestrength of this effect depends on the size of the basin of attraction of the pooling equilibriumoutcome.
∗Department of Economics, The University of Arizona, [email protected]†Department of Economics, The University of Arizona, [email protected]‡Department of Economics, The University of Arizona, [email protected]
1 Introduction
A lack of mutually understood terms to describe particular ideas can introduce frictions in
the ability of two parties to communicate. This is a common occurrence, for example, when
experts use jargon with individuals who only understand lay terms. Experts have a more
precise vocabulary to describe concepts in their field of specialty than do non-experts. For
example, a car mechanic might recommend that a cars’ regulator needs to be replaced if
the car is stalling frequently. The car owner may not be aware of what a regulator is, so
the term is meaningless to him. In such circumstances, the car owner’s decision amounts
to whether to believe and trust the suggestion from the car mechanic or not. As another
illustration, consider a doctor who informs a patient that he has a condition for which a new
experimental treatment is optimal, and for which the conventional treatment would be less
effective. The patient, unable to translate the data from medical tests into a diagnosis, has to
decide about whether or not to agree to the recommended treatment. If the patient suspects
that the doctor might be trying to mislead him into a more expensive treatment that is
no more effective than the conventional one, he might opt for the conventional treatment
instead. The costs of such instances of language incompleteness can be substantial, given the
economic value of situations in which there is interaction between experts and non-experts.
For example, 99.7 billion dollars were spent on auto repair in the US alone in US in 2008.
In 2014, 378 billion dollars were spent on prescription drugs.
The abstract, canonical, situation we have in mind is that of an expert (sender) advising
a decision maker (receiver) on the choice of a project to adopt. The project that is optimal
depends on the state of the world. Suppose that both sender and receiver have common
interests, in the sense that in each state of the world they agree on which project is optimal
given that state. Thus, if they have a common language in which they can describe each
state of the world, there are no incentive problems. It is an equilibrium for the sender to be
truthful and the receiver to believe the sender. Coordination on the optimal project results.
Suppose, however, that with positive probability the sender is language constrained and
that it is the sender’s private information as to whether or not this is the case. If she is
constrained, there are states of the world she cannot describe with her available messages in
a way that the receiver would understand. She may then be tempted to indicate a different
state, for which she has the appropriate message. She will do so, for example, if having some
project adopted is better for her than having no project adopted. Given that the language
constraint is private information, the receiver cannot be selectively trusting, and is better off
opting out of any project. Hence, communication may fail even when there is no language
constraint.
The key incentive problem is that a sender who lacks the proper language to describe the
optimal project may instead want to propose an inferior project that she can clearly describe.
1
If the receiver realizes this, and the payoff from the inferior project is less than from adopting
no project, he may be reluctant to adopt any project. This can make it impossible to get
the right project adopted even if the sender has the right message and uses it to propose
the right project. Indeed, as we show below, in the only plausible equilibria of the game, no
project is adopted, and any proposal of the sender is ignored. If it were common knowledge
that the language needed to describe all states were available, successful coordination on
the project appropriate for the actual state would be an equilibrium outcome. Thus, the
possibility of language incompleteness can lead to incentive problems, where there would be
none if it were common knowledge that such incompleteness were impossible.
In this paper, we report an experiment in which we consider whether the meanings of
expressions in a language erode in the face of such incentives. In our experiment, there is a
sender and a receiver. All plausible equilibria are inefficient and involve babbling on the part
of the sender. Thus, expressions of the language lose their meaning. However, substantial
gains can arise to all individuals if they are able to preserve the meaning of expressions
and link messages with their natural or focal meanings. Our experiment considers the
circumstances under which players can avoid such erosion of meaning. The experiment
consists of four treatments. Three of these have language incompleteness, and vary the
complexity of the environment. The measure of complexity is the number of states that the
language must try to describe. The fourth treatment has no language incompleteness. Unlike
in the seminal work of Crawford and Sobel [14], in which efficiency losses arise because expert
and decision maker disagree about the optimal action in each state of the world and therefore
the expert has an incentive to misrepresent the state of the world, in our experiment it is
only through language constraints themselves that incentive problems arise.
Our principal behavioral hypothesis is that initially, receivers will believe the messages
that they receive. However, over time behavior will converge to a pooling equilibrium in
which senders’ messages are not believed and receivers choose a safe, though inefficient
action. The results show that outcomes tend to converge toward a pooling equilibrium in
the relatively complex environment over time, supporting the hypothesis. On the other
hand, in our simplest environment, expressions of the the language retain their meaning and
both senders and receivers are able to attain earnings in excess of the pooling equilibrium
level. Finally, when it is common knowledge that the language is complete, full efficiency is
achieved.
A closer look at the data indicates the presence of some senders who are willing to behave
honestly at some cost to themselves. In the simplest environment, only a small fraction of
honest senders is required to make it optimal for receivers to believe the messages they
receive, while in the more complex treatments, a larger fraction must be honest. The actual
fraction of honest senders exceeds the threshold level in the simple environment but does
not exceed the critical percentage in the more complex environment. The willingness of
2
receivers to believe senders’ messages, coupled with the presence of a sufficient number of
honest players makes it possible for expressions of the language to retain their meaning and
for payoff levels that are greater than pooling equilibrium levels to be realized.
2 Background
A common language is an important driver of coordination and information processing in
organizations. While specialized “organizational codes” (Arrow [1]) facilitate communication
within the organization, they may create barriers to communication with the outside world.
Within organizations, “language compatibility” (March and Simon [24]) has an impact on
which communication channels are activated. If different areas within an organization have
their own specialized codes, it affects the patterns of communication and thereby the overall
performance of the organization. Therefore, it is important to understand how agents handle
communication tasks when they face language constraints. We implement such constraints
in the lab by endowing agents with codes that are individually rich enough to code every
element in the state space, but diverge with positive probability.
There is a wealth of evidence from the field on how language constraints inhibit commu-
nication and shape communication patterns. Tushman [29] studies communication patterns
in R&D settings and observes that “oral communication is effective only where a shared
coding scheme or language exists or where the actors are sufficiently alike in background
or perspective that they can rapidly develop a common language . . . Communication with
areas having different coding schemes may be less efficient, since it will have to overcome
an impedance or mismatch between the communicating areas.” Zenger and Lawrence [32]
find that age and tenure distributions in a firm affect communication patterns. Bechky [2]
documents misunderstandings due to differing occupational codes in manufacturing. Gali-
son [18] describes how scientific disciplines create trading zones to mediate communication
across subcultures within the disciplines. Our experiment can be viewed as capturing the
“impedance or mismatch” pointed out by Tushman.
Language constraints also reduce the effectiveness of expert advice. Experts using jargon
when communicating with non-experts is a common source of misunderstandings and missed
opportunities. Doctor-patient communication suffers from gaps between medical language
and everyday language. Doctors frequently fail to recognize patients’ attempts to switch
to medical language and doctors and patients have substantially different interpretations of
widely used psychological terms like “depression,” “migraine,” and “eating disorder” (Ong,
de Haes, Hoos and Lammes [25]). Williams, Davis, Parker, and Weiss [31] document the
limited “health literacy” of patients. They cite one study of hospital patients in which only
35% understood the word “orally,” 22% “nerve”, 18% “malignant,” and only 13% understood
“terminal.” According to Williams et al such deficiencies in health literacy have dramatic
3
impacts on health care costs. Our experiment embraces this expert-decision maker paradigm.
The expert has sufficiently many messages to label all states, as does the decision maker.
These labels, however, need not coincide, capturing the gap between the language of the
expert and that of the decision maker.
There are two types of formal models of language constraints, those with availability
constraints and others with symmetry constraints. Cremer, Garicano and Prat [16], Jager,
Metzger, and Riedel [20], and Sobel [28] study availability constraints, which consist of
restricted vocabularies. They consider common-interest games, so that it it meaningful to
study optimal strategy profiles. Cremer, Garicano and Prat are concerned with the design
of an optimal organizational code. The code is used to describe states that are drawn from
a known distribution. An optimal code is an optimal assignment of words to subsets of the
state space. The choice of an organizational code interacts with organizational structure
because there is a trade-off between the quality of communication within and across groups
in an organization. Blume [4] [6], extending ideas from Crawford and Haller [12], uses
symmetry constraints to describe situations in which some messages may be meaningless
to some of the agents. One use of this approach is to show how grammar can facilitate
language learning, the association of meaning to a priori meaningless messages (for a related
approach to thinking about structure in language see Rubinstein [26]). In our experiment
we implement both availability constraints, by having each language type only have access
to a subset of the message space, and symmetry constraints, by employing (at least initially)
meaningless messages in addition to focal message. Focal messages, in the sense of Schelling
[27]), provide a clue that makes it possible to agree on their interpretation. The co-occurrence
of both focal and meaningless messages is a feature of our experiment that is novel.
Blume and Board [7] introduce private information about language constraints, which
take the form of availability constraints: an agent’s language type is the set of messages
available to the agent. Each player’s private information is two-dimensional, described by
her payoff type and her language type. In sender-receiver games in which senders have
private information about which messages are available to them, receivers, who only care
about payoff relevant information, face a signal extraction problem. Receivers do not know
to what extent the message they observe is determined by the sender’s language type. This
produces a sense in which misunderstandings can arise in equilibrium, since payoff relevant
information is confounded by information about language competence. Blume and Board
show that this confounding of information about payoffs with information about language
is optimal in common-interest games (in contrast, say, to only using messages which are
commonly known to always be available). This line of work has recently been extended by
Giovannoni and Xiong [19]. Our experiment explicitly relies on this language-type paradigm.
Unlike in Blume and Board, in our experiment there is a distinction between focal and
meaningless messages, and a tension between efficient and focal message use.
4
Extant experiments involving language constraints focus either on the emergence of mean-
ing from initially meaningless messages or on the process of adapting natural language to
novel situations. Blume, DeJong, Kim and Sprinkle [3] (BDKS98) investigate the emergence
of meaning of messages in sender-receiver games inspired by Lewis [23]. They look at games
with two payoff states and enforce initial absence of meaning by randomizing over private
representations of messages. They find that in simple common-interest games with feedback
about population behavior, message meaning gradually emerges to the point where after 20
periods players are fully coordinated. Bruner, O’Connor, Rubin and Huttegger [8] (BORH)
obtain similar results without feedback about population behavior, having subjects interact
for more periods. Our experiment also uses meaningless messages, except that they are avail-
able concurrently with focal messages and that there is a temptation to use focal messages.
This temptation is a result of players’ agreeing only on the most preferred action in each
state, and not the entire ranking of actions, as in BDKS and BORH.
Krauss and Weinheimer [21] [22] experimentally study the evolution of reference phrases
for novel items (non-standard geometric objects). Subjects use free-form communication with
natural language as opposed to a restricted set of pre-fabricated messages. They find that
the length of a reference phrase used to describe a figure is inversely related to the frequency
with which it is mentioned and decreases over time. Reference phrases are shorter with
two-way than one-way communication. Weber and Camerer [30] use a picture identification
task to study cultural conflict and mergers in organizations. Senders describe office scenes to
receivers, using free-form communication. The sender is given pictures in a particular order
and describes them to the receiver. Payoffs depend on how quickly the receiver identifies
the correct order. Over time teams develop succinct descriptions for each figure and these
descriptions differ across teams. These conflicting languages create problems when teams
are merged. Post-merger completion times at first significantly increase, and while they drop
subsequently, they never achieve pre-merger levels. Weber and Camerer achieve mismatch of
codes, and as a result efficiency losses, by merging teams with team specific languages. We
impose mismatches by fixing the receiver language while privately randomizing the sender
language. Weber and Camerer document dramatic reductions in efficiency right after a
merger and a partial recovery thereafter. In our experiment, as reported in Section 5, we
observe a gradual decline in efficiency, as receivers learn to doubt the meaning of messages.
3 Theoretical predictions
In our experiment, we implemented three sender-receiver games, which differed in terms of
the number of payoff types of the sender, the number of actions available to the receiver,
and the distributions over sets of messages available to the two parties. There was also a
control treatment, in which the complete language was always available.
5
3.1 The game with three payoff states
One of the conditions we implemented used the payoff table shown in Figure 1. Each row
corresponds to one of three possible (payoff) states, A, B, and C. Each column represents
one of the four possible actions of the receiver. The actions W,X, and Y , can be thought of as
the adoption of one of three possible projects and the action Z as not adopting any project.
The actions W,X, and Y are optimal for both parties in states A,B, and C, respectively,
yielding a payoff of 10 to both players. The action Z represents choosing not to undertake
a project, and results in a sure payoff of 7 to both sender and receiver. If a project that
is inappropriate for the current state is undertaken, then the sender receives a relatively
attractive payoff of 9 while the receiver receives 0.
The timing of the game is as follows. The state is drawn from a uniform distribution.
The sender privately learns the true state (her payoff type). The sender then sends a message
to the receiver. After observing the sender’s message the receiver chooses an action. After
the choice is made, the receiver learns the state and both parties realize their payoff.
A
B
C
W X Y Z
10,10 9,0 9,0 7,7
9,0 10,10 9,0 7,7
9,0 9,0 10,10 7,7
Figure 1: The game with three payoff states
The prior probability of each payoff type is π(A) = π(B) = π(C) = 13. The message
space is M = {∗,#, a, b, c}. Using semantic evaluation brackets J·K, messages a, b and c
have focal meanings JaK=“The state is A,” JbK=“The state is B” and JcK=“The state is C,”
respectively. There is no prior specification of the meanings of ∗ and #, which we express
via J∗K = J#K =?.
In addition to her payoff type the sender privately learns her language type, the subset
of messages available to her. The language type space is Λ = {λa, λb, λc, λabc}, where λa =
{a, ∗,#}, λb = {b, ∗,#}, λc = {c, ∗,#} and λabc = {a, b, c}. Note that a sender always has
three messages and therefore as many messages as there are payoff states. The probability
of each language type is q(λa) = q(λb) = q(λc) = q(λabc) = 14, i.e. language types are equally
likely. Language types and states are drawn independently. The sender privately learns her
payoff and language type and sends a message from her language type to the receiver. After
seeing the sender’s message, the receiver takes an action W,X, Y, or Z.
6
3.2 Six payoff states and two payoff states
Another condition we implement has 6 payoff states. The payoff table is shown in Figure 2
below. As in the three-state setting, both players receive a payoff of 7 if action Z is chosen.
If the receiver makes an optimal choice given the actual state, both players earn 10. If the
receiver chooses an action other than Z that is not optimal in the current state, the sender
receives a payoff of 9 and the receiver receives 0. There are 7 language types, one containing
the full set of messages with focal meaning, and 6 others with one focal message and six that
are devoid of meaning.
A
B
C
D
E
F
T U V W X V Z
10,10 9,0 9,0 9,0 9,0 9,0 7,7
9,0 10,10 9,0 9,0 9,0 9,0 7,7
9,0 9,0 10,10 9,0 9,0 9,0 7,7
9,0 9,0 9,0 10,10 9,0 9,0 7,7
9,0 9,0 9,0 9,0 10,10 9,0 7,7
9,0 9,0 9,0 9,0 9,0 10,10 7,7
Figure 2: The game with six payoff states
The possible states are A,B,C,D,E, and F , and the available actions of the receiver
are T, U, V,W,X, Y, and Z. Payoff types are equally likely: π(A) = π(B) = π(C) = π(D) =
π(E) = π(F ) = 16. The message space is M = {∗,#,%,@,∧, a, b, c, d, e, f} with focal mean-
ings JaK]=“I am typeA,” JbK=“I am typeB” etc. and no prior specification of the meanings of
∗,#,%,@, and ∧. The language type space is Λ = {λa, λb, λc, λd, λe, λf , λabcdef}, where λa =
{a, ∗,#,%,@,∧}, λb = {b, ∗,#,%,@,∧}, λc = {c, ∗,#,%,@,∧}, λd = {d, ∗,#,%,@,∧},λe = {e, ∗,#,%,@,∧}, λf = {f, ∗,#,%,@,∧} and λabcdef = {a, b, c, d, e, f}. The language
type distribution assigns equal probability to all language types: q(λa) = q(λb) = q(λc) =
q(λd) = q(λe) = q(λf ) = q(λabcdef ) = 17. As in the three-payoff-state case, language types and
payoff types are drawn independently. The sender privately learns her payoff and language
type and sends a message from her language type to the receiver. After seeing the sender’s
message, the receiver takes an action.
The third parameterization we study has two payoff states, A and B. As before, both
players receive a payoff of 7 if action Z is chosen. If the receiver chooses an action other
than Z that is not optimal given the state, the sender receives a payoff of 9 and the receiver
7
receives 0 as shown in Figure 3.
A
B
X Y Z
10,10 9,0 7,7
9,0 10,10 7,7
Figure 3: The game with two payoff states
The two states are equally likely. The message space includes two messages with focal
meanings, a, and b, and one message ∗ without a focal meaning. The language type space
is Λ = {λa, λb, λab} with λa = {a, ∗}, λb = {b, ∗}, and λab = {a, b}.
3.3 Equilibrium Analysis
The sender-receiver games we consider have a finite set of payoff types Θ for the sender, a
finite set R of actions for the receiver, and a finite set of messages, M. There is a unique
action Z ∈ R that is the receiver’s best reply to beliefs concentrated on the (uniform) prior
π over the set of payoff types. There are two kinds of messages, messages whose meaning is
a (single) type and messages that are meaningless. We use semantic evaluation brackets, JK,to evaluate the meaning of each message. Let JK : M → Θ ∪ {?} be a mapping that assigns
either a meaning θ ∈ Θ to a message or declares the message meaningless. For each θ ∈ Θ,
let mθ be the message with meaning JmθK = θ. If a message m ∈ M is meaningless, then
JmK =?. We assume that for each θ ∈ Θ there is a message mθ in M. Thus, for each payoff
type θ in Θ there is a message mθ in the universe of all messages, M , whose meaning is θ.
In addition to her payoff type θ the sender privately learns her language type λ ∈ Λ =
2M \∅. Language types are drawn from a commonly known distribution q. The sender chooses
a message given the language she has available and the state she has observed. The sender
strategy σ : Θ × Λ → ∆(M) must satisfy the constraint σ(θ, λ) ∈ ∆(λ) for all θ ∈ Θ and
λ ∈ Λ. Given her language type λ and her payoff type θ, her strategy σ assigns probability
σ(m|θ, λ) to message m ∈ λ.
We say that σ is indicative focal if mθ ∈ λ ⇒ σ(mθ|θ, λ) = 1, and σ(mθ′ |θ, λ) = 0 for
all θ′ 6= θ and all λ ∈ Λ. This is the property that the sender is as truthful as possible. She
will indicate her type if her language allows her to do so and never pretend to be another
type. If her payoff type is θ and the message mθ whose meaning is θ, JmθK = θ, is available,
she will send message mθ; if her payoff type is θ and the message mθ is not available, she
will not pretend that her payoff type is θ′ by sending message mθ′ . In our experimental
condition with three states, for example, a plausible indicative focal strategy would be to
send messages a, b, and c, when the true state is A,B, and C respectively whenever the
8
message corresponding to the true state is available, and to send ∗ when the appropriate
message is not available.
The receiver’s strategy ρ : M → ∆(R) prescribes a probability distribution over actions
conditional on the message he has received. Thus, given any message m ∈ M , ρ(r|m) is
the probability that the receiver assigns to action r ∈ R. We restrict attention to games in
which the receiver has a unique best reply, rθ, whenever his beliefs are concentrated on θ,
and rθ 6= rθ′ for θ 6= θ′.
We say that the receiver strategy ρ is imperative focal if ρ(rθ|mθ) = 1 for all mθ. That
is, a receiver strategy is imperative focal if the receiver acts as though he is credulous in
response to meaningful messages. In response to any meaningful message mθ it assigns the
unique best reply to believing that the payoff type is θ.
The receiver’s strategy is said to be neutral if ρ(Z|m) = 1 for all m with JmK =?.
Under a neutral strategy, the receiver chooses Z in response to meaningless messages that
he receives. A strategy profile (σ, ρ) is neutral if ρ is neutral. Similarly, a (perfect Bayesian)
equilibrium (σ, ρ, µ), where µ denotes the belief system, is neutral if ρ is neutral.
A strategy profile (σ, ρ) is weakly focal if σ is indicative focal and ρ is imperative
focal. An equilibrium (σ, ρ, µ) is weakly focal if the corresponding strategy profile is weakly
focal.1 A strategy profile is focal if it is weakly focal and neutral. Thus, under a focal
strategy profile, the sender is as truthful as possible, the receiver is credulous after meaningful
messages and takes the pooling action after meaningless messages. Therefore, under a focal
strategy profile the sender always sends a message corresponding to the true state if it is
available and sends a meaningless message otherwise; the receiver responds to meaningful
messages with the unique best reply given the meaning of that message and responds to
meaningless messages with the pooling action.
Finally, an equilibrium (σ, ρ, µ) is a pooling equilibrium if ρ(Z|m) = 1 for all m that
are sent with positive probability in equilibrium.
We believe that neutral equilibria are the most plausible ones for the three experimental
conditions. The following result shows that all neutral equilibria must be pooling equilibria,
establishes that there are no focal equilibria, shows that the payoff from focal strategies
exceeds that from pooling equilibria and shows that there are non-focal equilibria with
significantly higher payoffs to both players than the pooling payoff. The bottom line is that
we predict pooling, even though both naive focal strategies and non-focal equilibria yield
higher payoffs than pooling.
1Note that an indicative focal equilibrium is imperative focal.
9
Proposition 1 In all three games:
1. All neutral equilibria are pooling equilibria.
2. The (common) payoffs from focal strategy profiles (9 in the two-state game, 8.5 in the
three-state game and 7.86 in the six-state game) exceed those from pooling equilibria (7
in all three games).
3. There are no focal equilibria.
4. There are equilibria in which the pooling action Z is not taken and payoffs exceed those
from pooling equilibria: Both the two-state and the three-state game have an equilibrium
with sender payoff 9.83 and receiver payoff 8.3. The six-state game has an equilibrium
with sender payoff 9.88 and receiver payoff 8.81.
Proof:
Part 1: In the two-payoff type game, suppose the receiver employs a neutral strategy, but
there is a message after which the receiver responds with an action other than action Z.
Without loss of generality, let that message be a. Then language type λa will send a re-
gardless of the payoff type, since the sender is always worst off if the receiver chooses Z.
The posterior probability on payoff type θ following message a is maximized if payoff type
θ sends message a when all messages are available, and no other payoff type ever sends a.
Suppose, again without loss of generality, that only payoff type A sends message a when all
messages are available. Then the posterior probability of the sender having payoff type A
following message a is 23< 7
10and hence the unique best reply to message a is action Z. A
similar argument holds for message b. The best response to any focal message is to play Z.
The argument for the three-and six payoff type games is nearly identical, except that the
maximal posterior probability on any payoff type is even lower than 23. Similar logic applies
to the 3-state and 6-state games.
Part 2: Consider state θ. For any language state λ with mθ ∈ λ the common payoff from a
focal strategy is 10. Otherwise, the common payoff from a focal strategy is 7. Since there
there is positive probability that mθ ∈ λ, the expected payoff exceeds the pooling equilibrium
payoff 7, which we know from Part 1 is the neutral equilibrium payoff. The common focal
strategy payoff is 9 in the two-state game, 8.5 in the three-state game and 7.86 in the six-state
game.
Part 3: Every focal equilibrium is neutral by definition. Therefore, it follows from Part
10
1 that a focal equilibrium has to be a pooling equilibrium. This is incompatible with the
equilibrium being imperative focal.
Part 4: We provide an example of a non-pooling equilibrium for each of the three games.
For the two-state game: Consider the following strategy profile : σ(a|A, λa) = σ(b|A, λb) =
1, σ(a|A, λa,b) = 12, σ(∗|B, λa) = σ(∗|B, λb) = 1, σ(a|B, λa,b) = 1
2, ρ(X|a) = ρ(X|b) =
ρ(Y |∗) = 1. Given the receiver’s strategy, the sender strategy is clearly optimal. Also, since
the posterior probability of payoff type B is one following message ∗, it is uniquely optimal
for the receiver to respond with action Y to message ∗. Finally, the posterior probability of
payoff type A after either message a or b is 34
and since 34× 10 > 7 it is (uniquely) optimal
for the receiver to respond to both messages a and b with taking action X. This shows that
(σ, ρ) is an equilibrium strategy profile. The sender payoff from this profile is 9.83 and the
receiver payoff is 8.3.
Three-state game: Consider the following strategy profile: σ(mθ|θ, λa,b,c) = 1 for all θ ∈Θ. σ(a|A, λa) = 1, σ(∗|B, λ) = 1 if ∗ ∈ λ, σ(#|C, λ) = 1 if # ∈ λ, σ(∗|A, λ) = σ(#|A, λ) = 1
2
if a 6∈ λ, ρ(W |a) = 1, ρ(X|b) = 1, ρ(Y |c) = 1, ρ(X|∗) = 1, ρ(Y |#) = 1. The sender’s strategy
is clearly optimal, given the receiver’s strategy. Following messages a, b and c the receiver’s
beliefs are concentrated on a single payoff type and his response is clearly optimal. Following
message ∗ the posterior probability of payoff type B is 34
and therefore action X is uniquely
optional. Following message # the posterior probability of payoff type C is 34
and therefore
action Y is uniquely optional. The sender payoff from this profile is 9.83 and the receiver
payoff is 8.3.
Six-state game: Consider the following strategy profile: σ(mθ|θ, λa,b,c,d,e,f ) =
σ(mθ|θ, λmθ) = 1 for all θ ∈ Θ. σ(∗|B, λ) = 1 if b 6∈ λ, σ(#|C, λ) = 1 if c 6∈ λ, σ(%|D,λ) = 1
if d 6∈ λ, σ(@|E, λ) = 1 if e 6∈ λ, σ(∧|F, λ) = 1 if f 6∈ λ, σ(∗|A, λ) = σ(#|A, λ) =
σ(%|A, λ) = σ(@|A, λ) = σ(∧|A, λ) = 15
if a 6∈ λ, ρ(T |a) = 1, ρ(U |b) = 1, ρ(V |c) = 1,
ρ(W |d) = 1, ρ(X|e) = 1, ρ(Y |f) = 1, ρ(U |∗) = 1, ρ(V |#) = 1, ρ(W |%) = 1, ρ(X|@) = 1,
ρ(Y |∧) = 1. Given the receiver strategy, the sender strategy is clearly optimal. Following
messages a, b, c, d, e, f the receiver’s beliefs are concentrated on a single payoff type and his
response is clearly optimal. Following message ∗ the posterior probability of payoff type B is56
and therefore action U is uniquely optional. The argument for the remaining messages, #,
%, @ and ∧ is the same up to exchanging the roles of payoff types and actions. The sender
payoff from this profile is 9.88 and the receiver payoff is 8.81. �
One implication of Proposition 1 is that, while focal strategies might be a sensible an-
choring point for initial play, they should not be able to persist in the long run, since they are
not equilibria. Our setup also makes it difficult for a priori meaningless messages to acquire
meaning. If a priori meaningless messages do not acquire meaning and play converges to
equilibrium in the long run, then only neutral and therefore pooling equilibria remain.
11
3.4 Level-k analysis
We think of the equilibrium described in section 3.3 as a description of the final state that
players might reach with sufficient experience with the game. In this section we consider
what might occur in the first few plays of the game, when players rely on introspection and
limited experience to formulate their strategies. They can be expected to be heterogeneous
in the conclusions that they reach and thus any model of initial play must allow variation
among players in decision making.
In many settings initial play can be understood in terms of level-k reasoning: Players have
models of their counterparts’ behavior of varying degree of sophistication and best respond
to the behavior predicted by these models. The least sophisticated model views other players
as naive non-strategic level-0 players. This is the model used by level-1 players. Thus, level-1
players best respond to level-0 behavior. Continuing in this vein, level-k players best respond
to level-k− 1 behavior for k = 1, 2, . . .. Cai and Wang [9] successfully adapt Crawford’s [15]
analysis of the communication of intentions to communication of private information. For
data from a sender-receiver game experiment that is inspired by Crawford and Sobel [14],
their analysis predicts over-communication, consistent with their observations.
A crucial step in any level-k analysis is the specification of level-0 behavior. It is standard
in communication games to anchor a level-k analysis at behavior consistent with a priori
message meanings. Thus, we let level-0 senders use an indicative focal strategy and random-
ize uniformly over meaningless messages when the message meaning for their payoff type is
not available. Similarly let level-0 receivers use an imperative focal and neutral strategy.
Then level-1 senders will send the message whose meaning matches their payoff type when
available and send the other meaningful message that they have given their language type
otherwise. Level-1 receivers use the same strategy as level-0 receivers. Level 2-senders use
the same strategy as level 1 senders. Level-2 receivers take action Z after all messages. In
prior work restriction attention to no more than three levels has proven useful. Camerer,
Ho, and Chong [10] find that their cognitive-hierarchy model, in which level-2 players best
respond to a mixture of level-1 and level-2 players, with an average level of 1.5 fits the data
of many games; Crawford and Iriberri [13] limit attention to three levels and observe a higher
proportion of level 1s than level 2s; and, Costa-Gomes and Crawford [11] find that the num-
ber of level 1s is approximately twice the number of level 2s. In line with these findings, we
adopt a rule-of-thumb that there are twice as many level-1s as level-2s and few level-0s as a
rough approximation for predicting initial play. Then we expect most senders to report their
payoff type truthfully if possible and to mimic another payoff type otherwise. Two thirds of
receivers are credulous and the remaining one third takes the pooling action Z in response to
a focal message. Therefore, relative to neutral (and therefore pooling) equilibria, we expect
over-communication in the initial rounds of play.
12
4 Experimental Procedures
4.1 Procedures and timing within sessions
The experiment consisted of 8 sessions that were conducted at the Economic Science Lab,
at the University of Arizona. There were three different conditions, the 2-state, 3-state, and
6-state conditions. Each session consisted of 120 periods in total and two conditions. Each
condition was in effect for 60 periods. On average, a session lasted for 90 minutes, including
initial instruction and final payment of the subjects. Instructions were read by a computer
in a neutral tone.
Some information about the sessions is presented in Table 1, including the sequencing of
conditions. The role of each player, as a sender or receiver, was fixed within each condition
but was always switched to the other role at the beginning of the next condition. Each player
was re-matched with another player in each period randomly. It was common knowledge
that, although interacting with the same group in the lab, the possibility of being matched
with the same participant in two consecutive rounds was small. Interaction was anonymous
in the sense that players could not associate a player with her action in any way that would
allow them to keep track of a player’s action.
Subjects were paid for every period, at a conversion rate of $1.00 per 37 points. Subjects
earned an average of 24 dollars. We recruited 118 subjects from the subject pool of the
Economic Science Laboratory at the University of Arizona. The pool is open for registra-
tion to full-time undergraduate students of the University of Arizona. We programmed the
experiment using z-Tree [17].
Upon arrival at their session, subjects were randomly assigned to computers in the labo-
ratory. At the beginning of each condition, one trial period was conducted to help subjects
better understand the experiment. The payoff in the trial period for each subject was re-
vealed, but was not counted in their final payment. During the 60 periods of each condition
that counted toward their earnings, subjects knew the period they were in and the number
of periods remaining. All earnings from the 60 periods were counted toward their payment.
In each period, subjects played a two-stage game. In the first stage, the sender observed
the true state of the world and the language set available, and then decided on the message
to send to the receiver. In the second stage, after receiving the message from the sender,
the receiver chose his action. Then both sender and receiver were told their own payoffs.
Messages were displayed on the screen in the same order for both players and this order was
constant over time. The history of states, messages and own payoffs in all previous periods
was available in a table on the sender’s screen for her to review. The history of messages,
action choices and own payoffs in all previous periods recorded in a table for the receiver
to review on is screen. For both players, this history information remained available at all
13
times.
Table 1: Session Information
Session Number Number of Subjects Periods 1 - 60 Periods 61 - 120
1 12 6-state 2-state
2 14 2-state 6-state
3 14 3-state 6-state
4 18 6-state 3-state
5 14 3-state 2-state
6 12 2-state 3-state
7 18 6-state 2-state
8 16 2-state 6-state
4.2 The conditions
4.2.1 The two-state condition
The 2-state condition allowed for two possible payoff states, A and B, which were equally
likely. The realized state was observed only by the sender. At the time the true state was
revealed to the sender, senders were also informed of the language they were able to use.
There were three possible language sets. The first one included a set of all the messages that
had a focal meaning, a and b, denoted here as language set {a, b}. The second and third
language sets consisted of one meaningless message *, and one message with focal meaning,
a or b. That is, the other two possible language sets were {a, ∗} or {b, ∗}. All three language
sets were equally likely to be available to a sender in a given period. Language sets, like the
states, were drawn independently each period and for each pair of players with the period.
After learning the state and the language they had available, each sender chose a message
from the available language set to send to the receiver she was paired with.
Receivers could not observe the true state they were in. The only information that
they had available to make their decisions was the payoff table, the history of their own
actions and payoffs, and the message they received from the sender they were matched with.
Both senders and receivers were provided with the payoff structure of the game. The payoff
structure of 2-state condition is shown in Figure 3 above. In the payoff table, the row
indicates the true state, and the columns the possible choices of the receiver. The numbers
14
in each cell are the payoffs to the sender and receiver respectively. Note that the only action
that senders take is to communicate with receivers. The payoff is determined entirely by the
receiver’s choice and the payoff state.
4.2.2 The 3-state and 6-state conditions
In the other two conditions, the number of language sets and decisions are larger than in
the two state condition, as shown in the Table 2 below. The payoff structures in the 3-state
and 6-state conditions have a similar pattern as in the 2-state condition, and are described
in Figures 1 and 2 above. In each condition, there is a number of language sets equal to the
number of states plus 1. The set of possible language sets always includes one set containing
all focal messages, with the remaining language sets consisting of one focal and a number of
meaningless messages equal to the number states minus one. In all conditions and for each
payoff state sender and receiver agree on the optimal action for that state. We refer to this
as the game being of common interest. If the receiver choses an action other than the safe
action Z, both players receive a payoff of 10 in one of the states, while in all other states,
the sender would receive a payoff of 9, and the receiver would earn zero. By playing the safe
action, the receiver ensures a payoff of exactly 7 to both parties.
Table 2: Condition parameters
Possible States Possible Language Sets
2-state A,B {a, b}, {a, ∗}, {b, ∗}
3-state A, B, C {a, b, c}, {a, *, #}, {b, *, #}, {c, *, #}
6-state A, B, C, D, E, F
{a, b, c, d, e, f}, {a, *, #, ˆ , @, %},
{b, *, #, ˆ, @, %}, {c, *, #, ˆ, @, %},
{d, *, #, ˆ, @, %}, {e, *, #, ˆ, @, %},
{f, *, #, ˆ , @, %}
4.2.3 Control condition
In 60 periods of sessions 9 and 10, a control condition was in effect. The payoff structure
was identical to that in the six state condition. However, it was common knowledge that
all senders always had the language set λabcdef available, and therefore, there existed a focal
equilibrium that yields a payoff of 10 to both parties. Comparing this treatment to the
6-state condition isolates the impact of language incompleteness.
15
5 Results
This section is organized in the following manner. In subsection 5.1, we consider aggregate
patterns in both sender and receiver behavior and how these evolve over time. We argue
that behavior moves closer to the equilibrium over time in the 6-state and 3-state treatment,
but fails to converge in the 2-state condition. In all conditions, there remain a fraction of
receivers who believe the messages they receive, as well as a fraction of senders who send
an honest message, even when they could benefit from lying. These latter two fractions are
great enough in the two state case to prevent convergence to equilibrium. We verify that
successful coordination occurs in the control condition.
In section 5.2, we report report the results from regresssions that investigate the deter-
minants of the behavior of individual senders and receivers. We find that they are influenecd
by both their experience in earlier periods, as well as by heterogeneous tendencies to be
honest or credulous. In section 5.3, we show that assuming a constant proportion of honest
individuals can account for the differences in outcomes across conditions. It is optimal for
receivers to believe senders’ messages if the probability that senders are truthful exceeds a
particular threshold, which differs among conditions. The threshold is lowest in the 2-state
condition and is exceeded by the actual percentage of honest individuals. In that condition,
this behavior generates payoffs to both parties well in excess of the pooling equilibrium level.
5.1 General Patterns in the Data
Our hypothesis is that behavior at the outset of play will have a distribution consistent with
a level-k model in which the levels range from 0 - 2. Senders’ behavior differs by level when
they lack the truthful message. Level-0 senders send a message devoid of meaning, while
levels 1 and 2, send a message with meaning. Receivers who are levels 0 and 1 follow the
recommendation of the sender, while receivers who are level 2 simply play the safe action Z.
Thus, if the distribution of levels is similar in the two roles, we would expect the percentage
of senders who lie to be greater than the percentage of receivers who play the safe action.
We calculate the percentage of senders who lie in the first five periods in the subset
of periods in which they to not have the truthful message available. This fraction is 0.410,
0.405, and 0.233 in the two, three, and six-state conditions respectively. The overall weighted
average is 0.317. For receivers, the percentage of individuals who, when they receive a
message with focal meaning, follow the action consistent with the message being truthful, is
77.78% in the 2-state, 55% in the 3-state, and 65.1% in the 6-state conditions, respectively.
for a weighted average of .684. Thus the data from initial play closely match our rule-of-
thumb prediction of two-thirds level-1 players and one-third level-2 players for receivers.
In the case of senders there are more truthful senders than our rule of thumb prediction
16
allows; we will return to this below and argue that there appears to be a robust contingent
of truthful types of senders.
Figure 4: Proportion of receivers who choose the safe action Z after receiving a focal message,last 60 periods
Figure 4 shows that receivers in the 6-state and 3-state conditions, who received a message
with a focal meaning, exhibit an increasing trend in their likelihood of choosing the safe
action. In the figure, the vertical axis is the percentage of observations in which Z is played,
averaged over all individuals. The horizontal axis is the period number, broken up into
5-period blocks. The data from the last 60 periods of each session is shown in the figure.
The increasing trend in the play of the safe action Z is less clear in 2-state case. Our rule
of thumb of two-thirds level-1 behavior and one-third level-2 behavior predicts that initially
one third of receivers take the pooling action Z in response to receiving a focal message.
This appears roughly consistent with the data, in terms of magnitude, though it does not
capture the modest difference in initial behavior between treatments.
The equilibrium analysis predicts that, in the long run, receiver behavior converges toward
the receiver taking the pooling action with probability 1 in response to all messages, including
focal messages. While there is not complete convergence in any of the three conditions, there
is a trend in this direction in the 3-state and 6-state conditions. There is no such trend in the
2-state condition: the percentage of receivers choosing Z in the last few periods is roughly
22% in the two-state condition, while it is above 2/3 in the other two conditions.
Sender behavior in the second half of the experiment is displayed in Figure 5. The top
panel shows the data from the 2-state case, and the middle and lower panels correspond to
the 3-and 6-state cases, respectively. The graphs in the left column indicate the percentage
of time that an individual told the “truth”, that is, she sent the message corresponding to
the true state, when she had the message available. This is indicated by the bar indicated
“Tell Truth”. The other two bars, “Lie” and “Neutral” are instances in which the individual
sent a message with focal meaning that did not correspond to the true state, and instances
17
Figure 5: Senders’ messages, when truth is or is not available, all conditions, all periods
in which she sent a message without focal meaning, respectively. These last two messages
were very rare when the focal message corresponding to the true state was available.
The panels on the right of Figure 5 contain the data from periods in which the message
corresponding to the true state was not available. In these cases, sending the truthful
message is not possible. The bar labeled “Lie” indicates the percentage of instances in
which the individual sent a focal message in cases in which the truth was not available, and
“Neutral” the percentage of the time in which a non-focal message was sent.
Figure 6 illustrates the same information for sessions in which the control condition was
conducted as one of the treatments. Recall that in the condition, all messages are always
available, so that senders can always tell the truth if they wish to. The upper panel shows the
behavior of senders under the control condition. It shows that the vast majority of senders, in
excess of 90%, send the message corresponding to the true state. The lower panels illustrate
the data from the 6-state condition, for the same sessions in which the control treatment was
conducted. These data resemble the pooled data from all sessions of the 6-state condition
shown in figure 5.
Figure 7 shows the time profile of the percentage of instances of lying over time when the
truth is unavailable. The data in Figure 7 indicate that there is no clear trend in senders’
lying behavior. Nonetheless, the increase in the tendency of receivers to choose Z over time
18
Figure 6: Senders’ messages in control condition, when truth is or is not available, allconditions, periods
Figure 7: Proportion of senders who lie over time when truth is unavailable, last 60 periods
19
suggests that senders’ messages are less likely to be believed over time.
Figure 8: Receivers’ average payoff over time, last 60 periods
Figure 8 shows the receiver’s payoff over time. In all three conditions, average payoff is
close to the equilibrium level of 7, though it is slightly greater in the 2-state condition, and
slightly lower in the 6-state condition.
Figure 9 illustrates the sender’s average payoff over time. In all three treatments, sender
earnings exceed the equilibrium level of 7. Earnings are greatest in the 2-state condition,
followed by 3-state and 6-state. In all three conditions sender earnings decline over time but
remain greater than the equilibrium level.
The pattern suggests that in the two-state condition there was sufficient successful co-
ordination so that both parties’ payoffs could exceed the equilibrium level. In the 6 state
treatment, senders’ earnings were greater than 7, while the receivers’ earnings were below.
This indicates that sender’s lies were frequently believed and this worked to the advantage
of senders. The increasing tendency of receivers to play the safe action Z in the 6-state
treatment is presumably a response to the adverse outcomes. In the 3-state and 6-state
condition, the average of senders’ payoff converges down towards the benchmark in 9. In the
2-state condition, this index shows a slightly downward trend.
5.2 Correlates of decisions of senders and receivers
We specified a number of regressions to study the determinants of a receiver’s choice of the
safe action Z. The estimates are given in Table 3 for all periods. The first three columns are
estimates from OLS regressions, while the last three are the results of logit regressions. The
dependent variable takes on value 1 if the receiver chooses action Z and 0 otherwise. Focal
message equals 1 if the sender sends a focal message and zero otherwise. BurnedLast10 is a
dummy variable that indicates whether the receiver got a focal message, chose an action as
20
Figure 9: Senders’ average payoff over time, last 60 periods
Table 3: Determinants of choosing the safe action Z for each condition
2-state 3-state 6-state 2 Logit 3 Logit 6 Logit
FocalMessage -0.569∗∗∗ -0.244∗∗∗ -0.258∗∗∗ -4.889∗∗∗ -1.696∗∗∗ -2.423∗∗∗
(0.0170) (0.0208) (0.0135) (0.240) (0.150) (0.138)
BurnedLast10 0.00667 -0.0288 -0.0242 0.213 0.196 0.171(0.0153) (0.0245) (0.0165) (0.156) (0.168) (0.144)
Period 0.00251∗∗∗ 0.00377∗∗∗ 0.00374∗∗∗ 0.0277∗∗∗ 0.0260∗∗∗ 0.0389∗∗∗
(0.000360) (0.000553) (0.000387) (0.00378) (0.00377) (0.00357)
cons 0.764∗∗∗ 0.614∗∗∗ 0.751∗∗∗ 1.989∗∗∗ 0.664 1.844∗∗∗
(0.0358) (0.0379) (0.0239) (0.450) (0.460) (0.383)lnsig2ucons 1.982∗∗∗ 1.605∗∗∗ 1.767∗∗∗
(0.236) (0.310) (0.244)N 2760 1740 2940 2760 1740 2940
Standard errors in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
21
if it were true, and the choice resulted in payoff of 0.2
The estimates show that receiving a focal message makes it less likely that a receiver
chooses Z, indicating that messages are believed at least to some extent. Receiving a focal
message in the two-state case makes the play of Z 57% less likely in 2-state, 24% in 3-state,
and 26% in 6-state. Being burned in the last ten periods has no effect. This means that
the increasing frequency of the play of Z over time is a general trend, rather than a series of
short-term changes as a result of receiving a recent payoff of 0. The coefficient on Period is
significantly positive in all conditions, revealing a trend toward greater play of Z. The trend
is slower in 2-state than in the other treatments. The estimates confirm the impression
from the figures that 2-state is more conducive to successful coordination than the other two
conditions.
Table 4: Fraction of time lying when truth unavailable
State Lying ratio when truth unavailable2 0.4828383 0.40534016 0.3153812
5.3 Explaining the patterns in the data
As we have seen, there is more honest behavior on the part of senders than would be con-
sistent with our level-k analysis or would be optimal given receiver behavior. The latter
is the case because both levels of the sender above 0 should lie, and it is not reasonable
to believe that many senders can be considered level-0s after playing this relatively simple
game for many periods. Moreover, there is a widespread tendency for receivers to follow
senders’ recommendations. In the two-state treatment, this combination of sender honesty
and receiver credulousness leads to payoffs higher than in equilibrium.
To account for this pattern, suppose that some senders prefer being truthful to lying,
in line with Crawford [15]. Define an honest sender as one who uses an indicative focal
strategy. Honest senders are truthful when truth is available and send a meaningless message
otherwise. In contrast, a strategic sender will send a message corresponding to the true state
if it is available and a focal message corresponding to another state when the true message
is not available.
The payoff to a receiver from playing action Z is always equal to 7 in all games. In each
of the conditions, there are s + 1 language types, where s is equal to the number of states.
2Using the number of times burned in the last 10 periods in the specification rather than a dummyvariable for whether one has been burned or not generates the same results in that the same variables aresignificant at the same thresholds of significance.
22
The true message is available in 2 of the s + 1 language profiles. Consider a situation in
which all senders are either honest or strategic. Denote the proportion of honest senders as
h, 0 ≤ h ≤ 1.
Figure 10 shows that a substantial fraction of senders are consistently honest or strategic.
The figure shows the percentage of instances, in the last 30 periods of each of the two 60-
period segments of the sessions, in which individuals lied and did not lie when the truth was
unavailable. The data are clustered at the boundaries indicating that a considerable share
of individuals behaved consistently.
Given the presence of both honest and dishonest types, the expected payoff to a receiver
of following the message equals
10 ∗ 2
s+ 1+ 7 ∗ s− 1
s+ 1∗ h+ 0 ∗ s− 1
s+ 1∗ (1− h) (1)
The first term is the payoff to the receiver from successful coordination, 10, multipled by
the probablity that the sender has the true message available in their language profile. The
second term is the payoff from the receiver playing Z in response to a message devoid of
meaning, if the sender is of an honest type. The third term is the payoff from following
the sender’s message, if it has focal meaning, the sender is dishonest, and the sender does
not have the true message available. This is compared to the payoff from not following the
message and playing it safe instead, which equals 7. The payoff from following the sender’s
recommendation is greater than that of playing Z if
h ≥7− 20
s+1
7 ∗ s−1s+1
(2)
In the three conditions of our experiment, s = 2, 3, and 6. Thus, the fraction of individuals
h that must behave honestly to make it optimal for the sender to believe the message is 14.3%
in the two-state condition, 57.1% in the three-state condition, and 82.4% in the six state
case. Table 4 indicates that in all three conditions, the percentage of instances in which the
sender lies is between 30% - 50%. This means that it is optimal for the receiver to believe
the sender in the two-state case and not to in the six-state and three-state cases, which is
consistent with the data.3
Another pattern that is apparent in Figure 10 is the greater incidence of lying in the two-
state case than in the other two environments. This is consistent with a greater benefit from
lying in the two-state case than in the other two. As Figure 4 shows, a greater proportion
of receivers believe the sender’s message in two-state than in the other environments. This
affects the relative expected payoffs from lying and from being honest. The proportion
3Figure 3 shows that there is some endogeneity in the extent of lying aversion. This is consistent withindividuals’ being more willing to lie if the private benefits from lying are greater.
23
of receivers whose choices are consistent with believing the message, is 0.70, 0.48, 0.38
respectively for 2-state, 3-state, and 6-state.
Figure 10: Ratio of sending messages honestly
We also calculate the potential lying cost for senders that would make them indifferent
between lying and being honest based on the proportion of receivers who chose the safe
option in the last 10 periods. The indifference conditions are as follows:
2-state:
0.70× 9 + 0.30× 7− 7 = 1.40 (3)
3-state:
0.48× 9 + 0.52× 7− 7 = 0.96 (4)
6-state:
0.38× 9 + 0.62× 7− 7 = 0.76 (5)
The threshold is lowest in the 6-state case, followed in turn by the 3-state and 2-state
conditions. This means that the cost that would make a sender indifferent between lying
and telling the truth is highest in the 2-state case and lowest under 6-state. Thus, if the
distribution of lying costs is similar in the three treatments, there would be more lying in
the 2-state treatment, than in the 3-state treatment, and the least lying should occur in the
24
6-state case. This pattern is consistent with the data and with the notion that the percentage
of players that is honest is endogenous.
6 Conclusion
In this paper, we have considered a setting in which language may be degraded over time.
The meaning of messages may erode. The potential opportunistic use of language on the
part of senders can create risks for receivers. If they naively follow the recommendations in
the focal language, and the sender tries to mislead them, receivers receive low payoffs. In
response, they ignore messages from senders, removing the incentive for senders to use the
language in a meaningful way. This equilibrium outcome comes at a cost to both players,
who would benefit if they could find a way to guarantee the truthfulness of the messages
that are sent.
We find that the complexity of the environment, measured in terms of the number of
possible states, is an important factor determining the extent to which language degrades
over time. In the six-state case, our most complex condition, behavior converged to close
to the pooling equilibrium outcome, as predicted. In the two-state case, messages largely
retained their meaning in the sense that opportunistic behavior was sufficiently limited to
make it profitable for receivers to believe the senders’ messages and respond accordingly.
While, at least for receivers, the data, at first glance, are consistent with a level-k model
in which there are two-thirds level-1 players and one-third level-2 players (consistent with
prior findings in the literature), we believe that there is more at work than heterogeneity in
rationality and beliefs. The data are also consistent with a fraction of individuals who have a
preference for behaving honestly. The game can be viewed as one in which there is an honest
type and a strategic type of the sender. The critical percentage of honest senders required to
make it optimal for receivers to follow the messages they receive is far lower in the two-state
case than the six-state. The data show that the critical value is exceeded in the two-state
case but not in the six-state case. Thus, the presence of a fraction of individuals who are
honest, coupled with a relatively small number of instances in which lying is profitable, leads
to a level of coordination considerably greater than would occur in equilibrium. This occurs
in the two-state case and the expressions in the language retain their meaning. On the other
hand, the percentage of senders who are honest does not exceed the threshold in the 3 and
6 state cases and, as a consequence, the meaning of expressions in the language do degrade.
25
Figure 11: Screen Shot for sender in 2-state condition
26
Figure 12: Screen shot for receiver in 2-state condition
27
References
[1] Arrow, Kenneth J. [1974], The Limits of Organization, Norton, New York NY.
[2] Bechky, Beth [2003], “Sharing Meaning Across Occupational Communities: The
Transformation of Understanding on the Production Floor,” Organization Science 14,
312-330.
[3] Blume, Andreas, Douglas V. DeJong, Yong-Gwan Kim and Geoffrey B.
Sprinkle [1998], “Experimental Evidence on the Evolution of Meaning of Messages in
Sender-Receiver Games,” American Economic Review 88, 1323–1340.
[4] Blume, Andreas [2000], “Coordination and Learning with a Partial Language,” Jour-
nal of Economic Theory 95, 1–36.
[5] Blume, Andreas, Douglas V. DeJong, Yong-Gwan Kim and Geoffrey B.
Sprinkle [2001], “Evolution of Communication with Partial Common Interest,” Games
and Economic Behavior 37, 79–120.
[6] Blume, Andreas [2004], “A Learning-Efficiency Explanation of Structure in Lan-
guage,” Theory and Decision 57, 265–285.
[7] Blume, Andreas and Oliver J. Board [2013], “Language Barriers,” Econometrica,
81, 781–812.
[8] Bruner, Justin, Cailin O’Connor, Hannah Rubin, and Simon M. Hut-
tegger [2014], “David Lewis in the Lab: Experimental Results on the Emergence
of Meaning,” Synthese 88,1–19.
[9] Cai, Hongbin, and Joseph Tao-Yi Wang [2006], “Over-Communication in Strate-
gic Information Transmission Games,” Games and Economic Behavior 56, 7-36.
[10] Camerer, Colin F., Teck-Hua Ho, and Juin-Kuan Chong [2004], “A Cognitive
Hierarchy Model of Games,” The Quarterly Journal of Economics 119, 861–898.
[11] Costa-Gomes, Miguel A., and Vincent P. Crawford [2006], “Cognition and
Behavior in Two-Person Guessing Games: An Experimental Study,” American Eco-
nomic Review 96, 1737–1768.
[12] Crawford, V.P. and H. Haller [1990], “Learning how to Cooperate: Optimal Play
in Repeated Coordination Games,” Econometrica 58, 571–595.
28
[13] Crawford, Vincent P., and Nagore Iriberri [2007], “Fatal attraction: Salience,
naivete, and sophistication in experimental hide-and-seek games,” The American Eco-
nomic Review 97, 1731–1750.
[14] Crawford, V.P.and J. Sobel [1982], “ Strategic Information Transmission,” Econo-
metrica 50, 1431–1451.
[15] Crawford, Vincent P. [2003], “Lying for Strategic Advantage: Rational and Bound-
edly Rational Misrepresentation of Intentions,” American Economic Review 93, 133–
149.
[16] Cremer, Jacques, Luis Garicano and Andrea Prat [2007], “Language and the
Theory of the Firm,” Quarterly Journal of Economics 122, 373-407.
[17] Fischbacher, Urs [2007], “z-Tree: Zurich Toolbox for Ready-made Economic Exper-
iments,” Experimental economics 10, 171–178.
[18] Galison, Peter [1997], Image & Logic: A Material Culture of Microphysics, The
University of Chicago Press, Chicago, IL.
[19] Giovannoni, Francesco, and Siyang Xiong [2017] ”Communication with Lan-
guage Barriers,” University of Bristol Working Paper
[20] Jager, Gerhard, Lars P. Metzger and Frank Riedel [2011], “Voronoi lan-
guages: Equilibria in cheap-talk games with high-dimensional types and few signals,”
Games and Economic Behavior 73, 517–537.
[21] Krauss, Robert M. and Sidney Weinheimer [1964], “Changes in the Length of
Reference Phrases as a Function of Social Interaction: A Preliminary Study,” Psocho-
nomic Science 1, 113–114.
[22] Krauss, Robert M. and Sidney Weinheimer [1966], “Concurrent Feedback, Con-
firmation, and the Encoding of Referents in Verbal Communication,” Journal of Per-
sonality and Social Psychology 4, 343–346.
[23] Lewis, David [1969], Convention: A Philosophical Study, Harvard University Press,
Cambridge, MA.
[24] March, James G. and Herbert A. Simon [1958], Organizations, John Wiley &
Sons, Inc..
[25] Ong, L.M.L., J.C.J.M de Haes, A.M. Hoos and F.B. Lammes [1995], “Doctor-
Patient Communication: A Review of the Literature,” Social Science & Medicine 40,
903–918.
29
[26] Rubinstein, Ariel [1996], “Why Are Certain Properties of Binary Relations Rela-
tively More Common in Natural Language?,” Econometrica 64, 343–355.
[27] Schelling, Thomas [1960], The Strategy of Conflict, Harvard University Press, Cam-
bridge, MA.
[28] Sobel, Joel [2015], “Broad Terms and Organizational Codes,” Working paper pre-
sented at ESSET 2015.
[29] Tushman, Michael L. [1978], “Technical communication in R & D laboratories: The
impact of project work characteristics,” Academy of Management Journal 21, 624-645.
[30] Weber, Roberto A. and Colin F. Camerer [2003], “Cultural Conflict and Merger
Failure: An Experimental Approach,” Management Science 49, 400-415.
[31] Williams, Mark V., Terry Davis, Ruth M. Parker, and Barry D. Weiss
[2002], “The Role of Health Literacy in Patient-Physician Communication,” Family
Medicine 34, 383-389.
[32] Zenger, Todd R. and Barbara S. Lawrence [1989], “Organizational Demogra-
phy: The Differential Effects of Age and Tenure Distributions on Technical Communi-
cation,” Academy of Management Journal 32, 353-376.
30