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You want to buy a used car, but the seller knows something you cannot: whether this one is a gem or a lemon. That single gap in information can be enough to shut the whole market down, good cars and all.

Adverse selection and screening

Hidden information about types, not hidden actions, is the problem here. When sellers know quality and buyers do not, any price attracts the worst goods that price will tempt out. Buyers know this and shade what they will pay, which drives even more of the good goods away, until the market can unravel completely.

From earlier lessons

Two quick ones before we start.

In a Bayesian game, uncertainty is about the other player's...

A buyer who cannot verify quality should price based on...

Predict, then play

Car quality is spread evenly from 0 to 100. A seller will part with a car only if the price covers its quality, and a buyer values any car at 1.5 times its quality, but cannot see it. Set a price and watch which cars come to market.

Why did that happen?

Take a guess, then reveal the reason

The price does not just set the terms of trade; it selects which cars appear. Offer a high price and you attract cars up to that quality, but the ones you draw in are, on average, only half as good as the price suggests, because quality is spread out below it. Buyers anticipate this and will pay only three-quarters of the price for the average car on offer. That shortfall holds at every price, so trade never happens. The information gap, not any villainy, empties the market.

The math

Quality $q$ is uniform on $[0,100]$ . A seller lists a car only if the price $p$ covers its value, so the cars on the market are those with $q \le p$ , whose average quality is $p/2$ . Buyers value a car at $1.5q$ , so their willingness to pay for the market’s average car is

1.5 \cdot \tfrac{p}{2} = 0.75\,p < p \quad\text{for all } p > 0.

Willingness to pay is below the price at every positive price, so the only price at which the market clears is $p = 0$ , where nothing of value trades. This is complete unraveling.

Definition, adverse selection and screening

Adverse selection is a hidden-type problem: the informed side (the seller) self-selects in a way that worsens what the uninformed side gets. It is distinct from moral hazard, which is a hidden-action problem. One remedy is screening: the uninformed party offers a menu designed so that different types choose different options. In insurance (Rothschild-Stiglitz), a menu of contracts trading premium against deductible leads low-risk and high-risk buyers to self-select, separating the types without anyone announcing them.

Work it out

Why no price clears, and how screening escapes it

Fix any price $p > 0$ . Sellers with quality above $p$ keep their cars, so only qualities in $[0,p]$ are offered, averaging $p/2$ . A buyer values that average car at $1.5 \times p/2 = 0.75p$ . Since $0.75p < p$ , the buyer refuses, so demand collapses at every positive price and the market clears only at $0$ .

Screening turns the problem around. Instead of one price, the uninformed side offers a menu. In insurance, pair a low premium with a high deductible and a high premium with a low deductible. Low-risk buyers, who rarely claim, prefer the cheap high-deductible plan; high-risk buyers prefer the fuller coverage. Each type reveals itself by its choice, so the menu separates types that a single price could not.

Key idea

When buyers offer too little under hidden quality, high-quality sellers leave first, reducing the average quality offered and pushing willingness to pay down again. A well-designed menu can screen types where a single price cannot.

Check yourself

Check yourselfapply

At a price of 80, what is the average quality of cars offered, and will a buyer pay 80?

Check yourselfanalyse

How does screening (an insurance menu) get around adverse selection?

Check yourselfbrings back: incomplete information

Adverse selection is often confused with moral hazard. What is the difference?

Sources

Akerlof, G. A. (1970). The market for "lemons": quality uncertainty and the market mechanism. Quarterly Journal of Economics, 84(3), 488-500.
Rothschild, M., and Stiglitz, J. (1976). Equilibrium in competitive insurance markets. Quarterly Journal of Economics, 90(4), 629-649.