Signaling Games: Communication When Words Are Cheap

Why do peacocks have such ridiculously large tails?

Why does a college degree help you get a job, even if you learned nothing useful?

Why do companies spend millions on Super Bowl ads that don’t describe their products?

Signaling theory provides the answer: When words are cheap, credible communication requires costly signals.

From biology to business, from education to dating, signaling games explain how information is transmitted when one party knows more than another — and has an incentive to lie.

The Information Problem

Many strategic situations involve asymmetric information:

• Sellers know product quality, buyers don’t
• Job applicants know their ability, employers don’t
• Companies know their prospects, investors don’t
• Animals know their fitness, potential mates don’t

The challenge: How can the informed party credibly communicate their type?

The problem: Cheap communication (just saying things) isn’t credible because everyone would claim to be high quality.

Solution: Costly signals that are easier for high types to send than low types.

The Basic Signaling Game

Players:

1. Sender (informed party): Knows their type (high or low)
2. Receiver (uninformed party): Observes signal, then acts

Sequence:

1. Nature determines Sender’s type (with some probability)
2. Sender observes their type, chooses a signal
3. Receiver observes signal (not type), forms beliefs, acts
4. Payoffs realized

Key question: When does the signal credibly reveal information?

The Spence Job Market Model

Michael Spence won the Nobel Prize (2001) for explaining how education signals ability.

Setup:

• Workers can be high ability or low ability
• Employers can’t observe ability directly
• Workers choose years of education $e$
• Employers observe education, then offer wage

Payoffs:

Worker utility:

• High type: $w - c_H \cdot e$ (cost $c_H$ per year of education)
• Low type: $w - c_L \cdot e$ (cost $c_L$ per year of education)

Key assumption: $c_H < c_L$ — education is less costly for high-ability workers

Employer profits:

• Productivity of high type: $P_H$
• Productivity of low type: $P_L$
• Wage offered: $w$

Competitive market: Wage equals expected productivity based on education signal.

Separating Equilibrium

Equilibrium where education perfectly reveals type:

High types: Get education level $e^* \geq \bar{e}$ Low types: Get no education (or $e < \bar{e}$)

Employer beliefs:

• If $e \geq \bar{e}$: Worker is high type, offer wage $w_H = P_H$
• If $e < \bar{e}$: Worker is low type, offer wage $w_L = P_L$

What is the minimum separating education level $\bar{e}$?

Conditions:

1. High types want to signal: $$P_H - c_H \cdot \bar{e} \geq P_L$$ (High type prefers getting degree and high wage to skipping degree and getting low wage)

2. Low types don’t want to mimic: $$P_L \geq P_H - c_L \cdot \bar{e}$$ (Low type prefers low wage with no degree to high wage with degree)

Solving:

From condition 2: $$c_L \cdot \bar{e} \geq P_H - P_L$$ $$\bar{e} \geq \frac{P_H - P_L}{c_L}$$

From condition 1: $$c_H \cdot \bar{e} \leq P_H - P_L$$ $$\bar{e} \leq \frac{P_H - P_L}{c_H}$$

Separating equilibrium exists if: $$\frac{P_H - P_L}{c_L} \leq \bar{e} \leq \frac{P_H - P_L}{c_H}$$

This works because $c_H < c_L$ (high types find education less costly).

Example:

• $P_H = 100$ (high productivity)
• $P_L = 60$ (low productivity)
• $c_H = 2$ (low cost for high types)
• $c_L = 5$ (high cost for low types)

Separating education level: $$\frac{40}{5} \leq \bar{e} \leq \frac{40}{2}$$ $$8 \leq \bar{e} \leq 20$$

Any $\bar{e}$ in this range (e.g., 10 years) achieves separation.

Key insight: Education may not increase productivity at all — it just signals pre-existing ability!

Pooling vs Separating Equilibria

Separating Equilibrium:

• Different types send different signals
• Receiver perfectly learns Sender’s type
• Signal fully reveals information

Pooling Equilibrium:

• All types send the same signal
• Receiver learns nothing from signal
• No information revealed

When do pooling equilibria exist?

If the signal cost is too high, even high types prefer to pool with low types and accept a lower wage rather than pay for education.

Example:

• If education costs 50 for high types, and the wage premium is only 40, high types won’t bother signaling
• Result: No one gets education, employers can’t distinguish types, everyone gets average wage

Market implications:

• Separating equilibria are efficient at information transmission but wasteful (costly signals)
• Pooling equilibria save signaling costs but create adverse selection problems

Costly vs. Cheap Signals

Costly signals:

• Expensive to produce
• More expensive for low types than high types
• Credibly reveal information

Examples:

• Education degrees
• Warranties (easier for high-quality products)
• Advertising spending (confidence in product quality)
• Peacock’s tail (only healthy males can grow large tails)

Cheap talk:

• Costless to produce
• Same cost for all types
• Not credible (everyone lies)

Examples:

• Used car salesman saying “It’s a great car!”
• Company claiming “We’re the best!”
• Dating profile saying “I’m amazing!”

However: Cheap talk can sometimes work if interests are aligned (more on this later).

The Handicap Principle (Biology)

Why do peacocks have such extravagant tails?

Zahavi’s Handicap Principle: Honest signals must be costly — especially costly to fake.

Peacock’s tail:

• Massive, colorful, hard to maintain
• Makes peacock slower, more visible to predators
• Only healthy males can afford this handicap
• Peahens prefer large tails because they signal good genes

Other biological signals:

• Roaring in deer: Only large, healthy males can produce deep roars
• Bright colors in birds: Require good nutrition and health
• Leaping in gazelles (stotting): Signals to predators “I’m so fit you can’t catch me”

Key principle: The signal must be a genuine handicap that low-quality senders can’t afford.

Advertising as a Signal

Puzzle: Why do companies spend millions on ads that contain no information about their products?

Example: Super Bowl ads that are just entertaining — no product details.

Signaling explanation (Nelson, 1974):

High-quality products:

• Customers will buy again and recommend to others
• Advertising brings in initial customers
• Future sales justify high ad spending

Low-quality products:

• Customers won’t buy again
• No repeat purchases or word of mouth
• High ad spending not justified

Result: Only high-quality firms can afford to spend heavily on advertising.

The ad content doesn’t matter — the cost of the ad is the signal!

Why this works:

• Signal cost: Same for all ($10M)
• Signal benefit: High quality gains repeat customers, low quality doesn’t
• Net benefit: Positive for high quality, negative for low quality
• Result: Only high-quality firms choose to signal

Modern version: Influencer marketing, brand sponsorships, premium placement — all costly signals of confidence in product quality.

Cheap Talk Games

Cheap talk: Costless, non-binding communication.

Crawford-Sobel Model (1982): When can cheap talk convey information?

Key insight: Cheap talk works when interests are partially aligned.

Example: Expert advice

• Expert observes true state (e.g., how serious your medical condition is)
• Patient chooses action based on Expert’s message
• Expert’s preferences depend on patient’s action

Full alignment: Expert wants exactly what’s best for patient → full information revelation possible (expert tells exact truth)

Complete conflict: Expert wants opposite of patient → no information conveyed (patient ignores expert)

Partial alignment: Expert somewhat biased → coarse information conveyed (expert gives general advice like “serious” vs “not serious”, but not exact details)

Real-world implications:

• Financial advisors: Cheap talk somewhat informative if incentives partially aligned (e.g., reputation concerns), but biased by commissions
• Political communication: Cheap talk mostly uninformative due to conflicting interests
• Recommendation letters: Cheap talk less informative than expected (everyone writes positive letters)

Commitment and cheap talk:

• If the speaker can commit to being honest (reputation, legal penalties), cheap talk becomes credible
• Audited financial statements are credible cheap talk (backed by threat of fraud prosecution)

Screening: The Receiver Moves First

Signaling: Informed party moves first (sends signal)

Screening: Uninformed party moves first (designs menu of contracts)

Example: Insurance companies

Problem:

• Customers know their risk (high or low)
• Insurance company doesn’t
• High-risk customers want more insurance

Solution: Screening menu

Contract A:

• High coverage, high premium
• Designed for high-risk customers

Contract B:

• Low coverage, low premium
• Designed for low-risk customers

Design constraints:

• High-risk prefer A to B (incentive compatibility for high-risk)
• Low-risk prefer B to A (incentive compatibility for low-risk)

Key difference from signaling:

• Signaling: Informed party pays cost to separate
• Screening: Informed party reveals information by choosing from menu

Other screening examples:

• Airlines: First class vs economy (business travelers choose first class)
• Software: Pro version vs free version (professionals choose pro)
• Warranties: Extended vs standard (high-use customers choose extended)

Credential Inflation

Problem: When many people can signal, the signal becomes devalued.

Education inflation:

• In the past, high school diploma signaled ability
• Now, bachelor’s degree required for many jobs
• Next: Master’s degree?

Why this happens:

• More people getting degrees → degree less informative
• Employers demand higher degrees to separate candidates
• Arms race: Everyone must signal more to stand out

Social cost:

• Everyone spends more on education
• No increase in actual productivity
• Pure waste: Resources spent just to maintain relative position

Solutions:

• Alternative signals: Work experience, portfolios, recommendations
• Skills testing: Direct assessment instead of credentials
• Apprenticeships: Learn while working

Countersignaling

Puzzle: Sometimes, the highest types deliberately avoid signaling.

Countersignaling: Sending a low signal to differentiate yourself from medium types who are desperately signaling.

Example: Luxury goods

• Middle class: Buy luxury goods with prominent logos (signal wealth)
• Truly wealthy: Buy luxury goods with no logos (too secure to need signaling)

Example: Academia

• Junior professors: Long CVs, list every publication
• Senior luminaries: Short CVs, only major achievements

Example: Tech industry

• Mid-level engineers: Long resumes, every skill listed
• Famous engineers: GitHub link, or just “worked on X at Google”

Why countersignaling works:

• Receiver knows only medium types feel the need to signal
• High types are secure enough to skip signaling
• Not signaling itself becomes a signal of extreme confidence

Conditions for countersignaling:

• Three or more types (low, medium, high)
• Medium types feel compelled to separate from low types
• High types are so obviously different they don’t need to try

Key Takeaways

1. Signaling games involve asymmetric information where one party tries to credibly communicate their type
2. Costly signals that are more expensive for low types can credibly separate types (education, warranties, peacock tails)
3. Cheap talk only works when interests are partially aligned, otherwise it’s not credible
4. Spence job market model — education signals ability even if it doesn’t increase productivity
5. Separating vs pooling equilibria — signals either reveal information or fail to distinguish types
6. Handicap principle — honest biological signals must be costly to fake
7. Advertising as signal — spending money on ads signals product quality through commitment
8. Screening — uninformed party designs menu to induce informed party to reveal type
9. Credential inflation — signaling arms race leads to wasteful over-investment in credentials
10. Countersignaling — highest types may deliberately avoid signaling to differentiate from medium types

Signaling theory shows that communication is most credible when it’s costly — and explains seemingly wasteful behaviors from peacock tails to PhD degrees as rational investments in information transmission.

Practice Problem

A startup founder is trying to signal to investors that their company is high quality. They have two options:

Option A: Spend $500K on a big launch event with celebrities and press coverage.

Option B: Offer investors a warrant that gives them extra shares if the company fails to hit revenue targets in 2 years.

Which is a more credible signal, and why?

This post is part of the Game Theory Series, where we explore the mathematics of strategic decision-making. Signaling theory reveals how costly actions can credibly communicate private information, explaining phenomena from education to evolution.