25. Signaling Models
Honest people don’t hide their deeds.
—Emily Brontë
In this chapter, we study signaling models. These models identify
conditions under which people send costly signals to reveal information or
their type. A person might signal wealth by purchasing an expensive piece
of art, physical stamina by climbing a mountain, or empathy by posting
support for causes on social media. Signaling to reveal status has always
been a part of human nature. In the nineteenth century, Thorstein Veblen
refined our understanding of signaling with his development of the concept
of conspicuous consumption: he observed that rather than buy goods that
bring direct enjoyment or practical utility, people often make choices to
signal their social status. Veblen would take delight in our modern icons of
conspicuous consumption, such as the Maybach Landaulet, an automobile
that retailed for nearly $1.5 million, ten-year-old bottles of Cristal that sell
for over $1,500 a bottle, and Leica cameras that sell for tens of thousands
of dollars.
Conspicuous consumption endures because we care what others think of us,
and what we consume signals our status to others.1 We do not see others in
their entirety, so we rely on what they wear, drive, and consume to make
inferences about their hidden attributes. If we see someone driving an
expensive car, we can infer that she has wealth. A person donating to a
charitable organization signals generosity—no selfish person would take
such an action. A person announcing her PhD in theoretical biology on
social media signals her intelligence and work ethic. Almost all actions
have some degree of signaling. When politicians vote whether to go to war
or to impose sanctions on another country, they signal ideologies.
Politicians with longer-term goals, such as running for president, may cast
votes that send the best signals rather than those that produce the best
policy.
In this chapter, we first study a discrete signaling model, in which an
individual can either send a signal or not. Individuals differ in their costs of

sending the signal. For signals to function, they must be costly or
verifiable. That will be a central take-away from this chapter. For example,
an employer may have a plum assignment in Barcelona, Spain, for the
summer and want to select from a collection of new hires, all of whom list
Spanish-language skills on their resumes. Claiming to speak Spanish is a
costless signal. Instead, the employer could create a language badging
program where earning the badge entails giving an hour-long presentation
in Spanish. For the employees who can speak Spanish, this signal (the
presentation) has low cost. For those employees not fluent in Spanish, the
costs of preparing an hour-long talk would be prohibitive. In the formal
language of signaling models, the badge separates the people who speak
Spanish from those who do not.
We then cover a continuous signaling model, in which signals can vary in
their magnitude. A summer camp may have only one position for a lead
kayaker and want someone with incredible stamina. The camp director
might then ask two applicants for the position to kayak as far as they can
over the next ten hours. The stronger of the two kayakers could choose a
distance that the weaker kayaker cannot achieve, guaranteeing that the test
separates. Both models give us conditions for when signals will separate
and when they will not. They therefore give us deeper insights than
anecdotal accounts of people, animals, politicians, and governments
signaling, by providing explicit characterizations of when they signal and
how costly those signals are. For example, the models will make clear why
students work so hard to signal their worthiness for college and medical
school. In the conclusion, we discuss the contributions of signaling models
as well as some other implications. We also discuss how signaling occurs in
ecology, anthropology, and business.

Discrete Signals
We begin with a discrete signaling model, in which a person decides
whether to take an action or not. You can buy an expensive watch to prove
wealth. You can major in physics to prove your intelligence. You can swim
the English Channel to prove your physical health. You cannot go halfway:
you either send or do not send the signal. The model assumes two types of
people, denoted as strong and weak. The types could correspond to

physically fit or unfit marine recruits, or monolingual and bilingual
employees.
The cost of sending the signal, which might be engaging in a fitness
regimen for a month for a potential marine or the aforementioned
presentation in Spanish for the job applicants, depends on a person’s type.
Strong potential marines find it less costly to complete the fitness regimen.
In the model, we assume that everyone who sends the signal shares equally
in the total benefit. This assumption can be interpreted in either of two
ways. In some cases a resource might be split among those who send the
signal. For example, everyone who donates $1,000 to a school (a signal of
generosity) may get their name on the wall. In other cases, such as for the
marines and job applicants, the winner(s) of some prize may be randomly
chosen from the set of people who send the signal.
The model supports three types of outcomes: pooling, where everyone
sends the same signal; separating, where each type sends a unique signal;
and partial pooling, where some types separate and others do not.

Discrete Signals Model
A population of size N consists of S strong types and W weak types whose
costs of sending a signal are c and C respectively, with c < C. Those
members of the population who send the signal equally divide a benefit of
B > 0. The model has three possible outcomes:
Pooling

image: Both types signal.

Separating (c <

image and

image < C): Strong types signal.

Partial pooling (c < image < C <
of the weak types signal.

image): Strong types and a fraction

In the model, we assume that individuals make optimal choices given the
actions of others. That is, we treat this as a game and solve for an
equilibrium. In the pooling equilibrium, everyone sends the signal. This
equilibrium exists when the benefit is high and the cost for the weak type to

send the signal is low. The exact condition is that the benefit divided by the
number of people must exceed the cost for the weak type. Suppose that a
benefactor donates $1 million for student scholarships to be split among all
graduates of a high school with 100 students. Suppose that 50 of the
students are weak and 50 are strong and that a strong student can graduate
from high school by studying two hours per week, while a weak student
must put in ten hours. We can approximate the costs of studying to be
$2,000 for the strong students and $5,000 for the weak students. If all 100
students graduate, each receives a $10,000 scholarship. Given these
assumptions, it makes sense for both types of students to study.
Suppose, though, that we reduce the size of the scholarship pool to
$200,000. Now, if all of the students graduated, each would receive only
$2,000. Studying is no longer in the weak students’ self-interest. It still
makes sense for the strong students, who now each receive $4,000. That
amount is still not sufficient to induce even a single weak student to
graduate (the second condition in the box above). In this case, the
scholarship offer produces separation.
Last, suppose that the scholarship pool contains $400,000. Once again, if
everyone graduated, the weak students would receive less than their $5,000
cost of studying. It follows that they would not all choose to study.
However, if none of them studied, the strong students would each receive
$10,000. That amount would be enticing to the weak students. In
equilibrium exactly 30 of the weak students graduate along with all 50
strong students. In total, 80 students graduate, and each receives $5,000, the
costs of studying for a weak student. We refer to this outcome as partial
pooling, as only a portion of the weak students pool with the strong
students.
The partial pooling equilibrium is more complicated than the others as it
requires coordination among the weak students. We could assume that there
exists some process by which weaker students communicate to others that
they plan to take actions that ensure graduation. Or, we could assume that
the weaker students put in just enough effort so that whether they graduate
is a random event such that, on average, 30 of them graduate. This second
scenario seems less plausible. In general, we should interpret partial

pooling equilibria as benchmarks, as what would happen if people
optimized. Whether a partial pooling equilibrium is attained likely depends
on the situation, in particular, on whether people can communicate intended
actions.

Continuous Signals
In the partial pooling equilibrium of the discrete signals model, the strong
types may feel frustration. If they could send a strong signal, they could
separate fully from the weak types and earn a higher payoff. To include that
possibility in the model, we can alter our assumptions and allow the strong
types to choose the magnitude of the signal they send. This requires only
slight modification in our model. We reinterpret the costs of sending the
discrete signal as a cost per unit of the continuous signal. We assume that
for any fixed amount of the signal, the strong types have a lower per-unit
cost of signaling.
To create separation in this new model, the strong types must be willing to
choose a magnitude that is prohibitively costly for the weak types, yet still
worth sending given the benefits and the costs. Reasoning through the
model, we find that at least some of the strong types, though not necessarily
all, can separate themselves from the weaker types.
Surprisingly, the magnitude of the signal the strong types must send
becomes smaller as the size of the strong group increases. This occurs
because the benefits to a weak type of sending the signal decrease in the
size of the strong group. Being part of a larger group provides fewer
benefits. The condition for full separation implies that it will be more likely
when there are few strong types or when the strong types have much lower
costs of signaling.

Separation with Continuous Signals
A population of size N consists of S strong types and W weak types with
per-unit costs of signaling c and C > c, respectively. The individuals who
send the largest signal split a benefit B. Any signal of magnitude image

separates the strong types. If CW ≥ cN, then all of the strong types
separate. If not, a partial pooling equilibrium exists in which a portion of
the strong types signal.2
This model can explain why expensive watches and jewelry function as
signals of wealth. A person’s house or car also signals her wealth, but
people cannot carry their houses and cars around with them at all times.
Clothes can signal wealth as well, but may not be able to create separation.
For a few hundred dollars, a person could dress like someone of significant
wealth. Watches and jewelry, because of their high costs, are more effective
as signals. A poor or middle-class person could not afford a $10,000 watch.
By wearing one a person proves she has wealth. The benefit she derives
may be that people treat her with more respect—assuming that people see
wealth as correlating in some way with importance (an inference we might
question).

The Uses and Value of Signals
We signal in an attempt to reveal hidden attributes to others. We take
actions to signal our fitness, wealth, intelligence, and generosity.
Sometimes our actions produce signals as by-products. A person who
competes in marathons for the pure joy of running signals fitness and
dedication even if that was not her intent. The signaling model provides an
alternative lens for interpreting a large number of actions. Did a person
choose to attend an event, master a skill, or purchase an item out of
personal interest, or to signal a type? We might not be able to distinguish
between the two cases.
Signaling models also provide alternative explanations for empirical
regularities—even for the value of earning a college diploma. Data on
incomes show that college graduates earn significantly higher salaries. We
could infer that the higher wages result from skills and knowledge acquired
at college. That data also show that math and science majors earn even
higher salaries. From that we could infer that the skills learned in those
majors have greater economic value. However, if we look at the tasks that
math majors perform, we may find that few use calculus. Moreover, almost
no one interviewing for a job is ever asked the derivative of the cosine

function or to explain Boyle’s law. In light of that, we might infer that
college degrees in general and science and math degrees in particular
represent signals of a person’s ability to acquire knowledge. The higher pay
that graduates receive stems entirely from the signaling value of degrees
rather than what the graduates have learned.3
Consider the signaling required to become a doctor. Students must pass
classes in physics, organic chemistry, and calculus. But do doctors use any
calculus? Has your doctor ever looked in your ears and nose and then
scratched a calculus equation on her notepad? Of course not. Knowledge of
calculus, for the most part, may not be relevant to being a doctor, but it may
be a good signal of the ability to master a corpus of knowledge. If so,
passing calculus becomes a useful signal even though the subject material
has little direct relevance.
When constructing institutions or rules in which people send signals, we
would prefer the actions that produce signals build useful skills. To be a
successful doctor, a person must be able to memorize facts. To signal the
ability to memorize, one could require that applicants memorize the
capitals and currencies of every country. Success would signal a candidate’s
ability to memorize but would be functionally useless. When rushed to the
emergency room with a strange feeling in your stomach, you would not
care if your doctor knew that Bratislava is the capital of Slovakia, but you
would want your doctor to know the various parts of the digestive system.
For this reason, medical boards require that doctors pass exams on
anatomy. Passing anatomy signals the ability to memorize. More important,
knowing the parts of the body is useful for those who do pass. Thus,
passing the anatomy exam provides a functional signal.

Summary
The signaling model can be applied widely. As already noted, the peacock’s
feathers signal robust health. Otherwise, the decorative fans of feathers
have little functional value. They may, in fact, be worse then useless. Far
better that the peacocks had chosen to develop stronger talons. Strong
talons would be more difficult for peahens to notice from afar, so tail

feathers won out evolutionarily.4 The colorful rear ends of male fruit flies
serve a similar function as the peacock’s feathers, as does the chirping of
grasshoppers and birds. Chirping takes energy. Only a well-fed grasshopper
can devote time to chirping rather than chasing down food. Hence, chirping
functions as a signal.
Human societies engage in a variety of actions to signal their fitness.
Anthropologists differentiate between three forms of costly signals:
unconditional generosity, wasteful subsistence behavior, and craft
traditions.5 The potlatch, a ritual carried out by the indigenous people of
the Pacific Northwest, may be the most salient example of signaling
generosity. To celebrate an event, say a birth or death, a chieftain would
give away (or destroy) great amounts of wealth and would challenge other
chiefs to match those amounts. Failure to match was a loss of prestige.
Giving away wealth can be seen as socially good, but burning it is wasteful.
Wasteful subsistence behavior occurs whenever people, typically men,
choose to engage in hunting behaviors with lower expected payoffs than
harvesting seeds or berries. The men do so because they earn extra respect.
The successful hunter signals his strength and bravery, which could be
useful in other settings. The successful berry picker signals good eyesight
and patience—useful traits, to be sure, but not as predictive of certain types
of fitness as turtle-hunting skill. A study of the Meriam, who live on a
group of islands of northern Australia, found that male turtle hunters had
more than twice as many surviving offspring at age fifty as non-turtlehunters.6
Relatedly, many craft traditions involve commitments that require sufficient
time and resources. These activities can result in useful objects—blankets,
for example. Craft traditions also involve the making of ceremonial objects
that have little practical value. Some anthropologists interpret their creation
as signaling. The meaning that accrues to such objects—they can be
endowed with substantial cultural significance—need not depend on their
functionality.
Some advertising also can be interpreted as costly signaling. By purchasing
an expensive Super Bowl commercial, a company signals legitimacy. It

implies that it believes consumers will like its product enough for the
company to earn back the cost of the advertisement in profits. For example,
imagine that two manufacturers each introduce a new coffeemaker. One of
the manufacturers knows it has a superior product. The other knows that
despite the best efforts of its engineers, its product is likely to break down
and leave customers less than satisfied. This second manufacturer expects
to have 20% of its products returned.
Millions of people may buy a coffeemaker during a given year. Without
advertising, the two firms might well split the market. Suppose that the
manufacturer of the better product spends $2 million on an advertisement
to signal the quality of its product. The manufacturer anticipates that early
purchasers will buy the product and, in the long run, that this will lead to
more sales. The manufacturer may well have a version of the Polya Process
model in her head. In contrast, the manufacturer of a lousy product would
not take out such an advertisement because its product has little chance of
large sales. Spending money to signal product quality is sometimes referred
to as burning money. Burning money attracts buyers much as the peacock’s
feathers attract mates.
In all of these cases, signaling involves a cost. Those who send the signal
find that the benefits of identifying their greater wealth, ability, or even
generosity are reduced by the cost of the signal. In addition, the time and
effort spent signaling can be thought of as opportunity costs: resources
could have been used in some other way, perhaps creating greater social
surplus. For example, a teenager may spend hours deciding which clothes
to wear so as to signal his social awareness or devote time to nonproductive
activities that he believes will improve his chances of acceptance at an elite
college.
To make signaling less socially costly, we try to make signals as functional
as possible. Better to have young people signal their physical fitness and
bravery by playing team sports, where they learn rules of sportsmanship
and collective interests, than to have them risk death jumping motorcycles.
As previously noted, better to require doctors to memorize human anatomy
than a random collection of J. R. R. Tolkien’s Elvish languages.
Nevertheless, try as we might, wasteful signaling will persist. Our

challenge is to use models—in particular, the tools of mechanism design—
to construct institutions and protocols so that the signals people send are as
functional as possible.