Lecture 23: Asymmetric Information - Signaling and Silence

What this lecture covers

The lecture opens the course's final unit on asymmetric information by studying two settings where one side of an interaction knows something the other does not. In the first half, using a Cournot competition example where a firm's costs are verifiable and can be freely disclosed, it shows that information tends to unravel: because low-cost firms want to reveal their advantage, and firms that stay silent get assumed to be worse than average, every type except the very worst ends up revealing itself, and even the worst type gets effectively identified by its silence.

In the second half, the lecture turns to information that cannot be verified directly, such as whether a worker is genuinely skilled, and builds the Spence signaling model of education from scratch. It shows why cheap talk (just claiming to be a good worker) fails, and why a costly signal, education, can work only if it is differentially costly for good and bad workers. After watching, you should be able to explain why silence can be informative, construct and check a separating equilibrium, and state why this model of education is often described as pessimistic.

Key ideas

• Verifiable information: information that can be costlessly and credibly disclosed (audited costs, exam certificates) tends to unravel because failing to disclose signals the worst possible type.
• Informational unraveling: if the best type reveals itself, then the next-best type must also reveal to avoid being mistaken for worse types, and so on, until even the worst type is effectively revealed by staying silent.
• Silence can be informative: the absence of a signal conveys information when receivers know the signal was available and would have been used by better types.
• Cheap talk fails: unverifiable claims that are equally easy for any type to make (dancing on a table and saying "I'm a good worker") carry no information because a bad type could make the same claim just as easily.
• Costly signaling: a signal works only if it is more costly (in effort, not just money) for the type that shouldn't send it than for the type that should.
• Separating equilibrium: an equilibrium where different types choose different observable actions, and outside observers' beliefs about what each action means are consistent with what each type actually does.
• Consistency of beliefs: an equilibrium requires that observers' inferences from behavior match what is actually happening in that equilibrium, not arbitrary beliefs.
• Signaling versus learning: in the model presented, education does not raise anyone's productivity; it only lets pre-existing good workers separate from bad workers, which is why the model is called pessimistic.

Walkthrough

Verifiable costs and why low-cost firms disclose (0:01)

Using a Cournot duopoly where one firm's cost type (high, medium, or low) is private but verifiable, the lecture builds up the logic step by step through student answers: a low-cost firm wants to reveal itself because it makes the rival produce less; a medium-cost firm then also wants to reveal itself to avoid being mistaken for high cost; and once both lower types reveal, a high-cost firm is effectively revealed by its silence even though it never explicitly discloses.

Information unraveling and the value of silence (11:41)

The lecture generalizes the three-type example to any number of types and names the phenomenon information unraveling. It uses the Sherlock Holmes story of the dog that didn't bark to illustrate that the absence of an expected signal can itself be highly informative, provided the receiver knows the signal was available.

Real-world examples of unraveling (16:44)

The lecture walks through several everyday cases of the same logic: American resumes that list even trivial achievements because omission implies having done nothing notable; Los Angeles restaurants displaying health inspection grades down to low grades because omitting the certificate would imply the worst grade; and a proposed university policy that would have let students selectively disclose only good Credit/D/Fail grades, which the lecture argues would unravel into the grade effectively meaning the lowest possible outcome.

Unverifiable information and the failure of cheap talk (24:59)

Shifting to information that cannot be verified, the lecture uses the example of a job interview question ("are you interested in working here?") to show that an answer costing nothing to give, and equally available to any type, carries no informational content. It generalizes this to the problem facing genuinely good workers who want to convince an employer they are good but cannot simply say so credibly.

Building the Spence education-signaling model (28:59)

The lecture sets up a labor market with good workers (productivity 50) and bad workers (productivity 30), competitive wages, and a claim that an MBA degree can serve as a signal if it is cheaper, in effort rather than tuition, for good workers than for bad workers. It proposes a candidate equilibrium where good workers get a three-year MBA, bad workers do not, and employers pay MBA holders 50 and non-MBA holders 30.

Verifying the separating equilibrium (42:31)

The lecture checks the proposed equilibrium formally: it confirms employer beliefs are consistent with behavior, then checks that neither worker type wants to deviate. Good workers earn 35 (50 minus three years of cost 5) by getting the MBA versus 30 by not getting it, so they comply; bad workers earn 30 by not getting the MBA versus about 20 by getting it (50 minus three years of cost just over 10), so they also comply. This confirms a valid separating equilibrium.

How long the signal must be (52:51)

Testing whether a one-year MBA could also separate types, the lecture shows it fails: with only one year of cost, bad workers would find it worthwhile to get the degree too (earning about 40 versus 30), collapsing the separation. It concludes the degree length (or difficulty) must be large enough that the cost difference between types is sufficient to deter bad workers, illustrating why signals need meaningful cost gaps, not just any cost.

Lessons about education and inequality (59:59)

The lecture draws out broader implications: making credentials easier to obtain triggers qualification inflation as good workers seek new ways to separate themselves. Taken literally, the model implies education adds no productivity, wastes real resources, and can widen inequality by lowering the average pay for those without access to costly signaling, since employers who can no longer identify good workers pay everyone the pooled average.

Before you watch

• Review the Cournot competition model and best-response/reaction curves from earlier in the course.
• Recall the concept of strategic substitutes, since it explains why a low-cost firm benefits from revealing its type.
• Be comfortable with basic Nash equilibrium reasoning, since this lecture extends it to equilibria involving types and beliefs.

Check your understanding

1. Why does a medium-cost firm choose to reveal its costs even though only the low-cost firm has an obvious incentive to disclose?
2. What makes silence informative in the unraveling examples, and why does this depend on the receiver knowing that disclosure was possible?
3. Why does simply claiming to be a good worker fail to convey any information to an employer?
4. In the Spence model, what two conditions must hold for a proposed separating equilibrium to actually be an equilibrium?
5. Why does a one-year MBA fail to separate good and bad workers in this model, while a two-year MBA succeeds?
6. In what sense does the lecture describe this model of education as pessimistic, and what does it imply about education's effect on inequality?