Adverse Selection Explained Through an Interview Game

Adverse selection means the counterparty willing to trade with you already knows something you do not, and a used car game proves it.

Adverse selection happens when the party willing to trade with you is more likely to trade specifically because they know something you do not, which means the average trade you get filled on is worse for you than the average trade available in the wider market. Interviewers test this with a simple game: you set a price for an item of uncertain value, a counterparty who knows the true value decides whether to trade with you, and you have to reason about what accepting or rejecting that trade reveals.

A standard version of the game: you are buying a used car of value between $0 and $10,000, uniformly distributed, and the seller knows the exact value while you do not. You name a price, and the seller sells only if your price is at or above the car's true value to them. The question is what price you should offer.

If you offer $5,000, expecting to get a car worth $5,000 on average, you are wrong. The seller only accepts when the true value is at or below $5,000, so among the cars you actually end up buying, the value is uniformly distributed between $0 and $5,000, averaging $2,500. You paid $5,000 for a car worth $2,500 on average, a loss of $2,500 per trade, purely because the fact that the seller accepted your offer changes what you should believe about the value.

Since any price you name only attracts sellers whose cars are worth less than or equal to that price, and the average value of an accepted car is always half of your named price under a uniform distribution, the expected value of the car you receive is always half of what you paid. This means every positive price you could name loses money on average, and the only price that does not lose money is $0, at which point no trade happens at all. This version of the problem, first described by the economist George Akerlof, is why a market can unravel entirely once one side has persistently better information than the other.

Interviewers want to see you reach this conclusion through the conditional reasoning, not simply recall that the answer is zero. Stating that the accepted trade set is not a random sample of all possible trades, and working out its true conditional average, is the actual skill being scored.