Adverse Selection: Pooling and Separating Equilibria

Rothschild and Stiglitz (1976) showed that in insurance markets with private information about risk type, no pooling equilibrium can survive cream-skimming entry -- a competitor can always profitably attract just the low-risk customers. The only stable equilibria are separating equilibria, where contract design induces different types to self-select. The cost of separation is the under-provision of coverage to the low-risk segment, which receives less insurance than it would in a full-information world.

Worked example with round fictional numbers. Suppose half the population has a 5 percent annual claim probability (low-risk) and half has a 25 percent annual claim probability (high-risk). The actuarially fair pooled price is 15 percent of expected loss. If the insurer offers a single pooled contract, low-risk customers (whose fair price is 5 percent) overpay by 10 percentage points and many exit. Now offer two contracts: full coverage at a price of 25 percent, and a partial-coverage contract with a $1,000 deductible at a price of 5 percent. High-risk customers prefer the full-coverage contract (the deductible exposure outweighs the premium savings); low-risk customers prefer the partial-coverage contract. The market separates and both segments stay insured -- but the low-risk segment carries deductible risk it would not have to bear under full information.

Pooling equilibria are unstable in voluntary markets but can be sustained by mandate. The individual mandate in the Affordable Care Act, employer-sponsored coverage, and Social Security all force pooling by removing the exit option for low-risk participants. Without these mandates, every voluntary insurance market eventually unravels toward the high-risk pool -- which is why repealing or weakening mandates often triggers premium spirals in the affected market.

The separating-equilibrium framework generalizes far beyond insurance. Labor markets use education credentials as a separating signal (high-productivity workers can credibly signal by investing in costly education that low-productivity workers find too costly to mimic). Credit markets use collateral and down-payment requirements as separating devices. Private-fund secondaries use GP-led continuation structures to separate long-horizon LPs from liquidity-sensitive ones. In each case, the contract design is doing the work that transparent pricing cannot, because the buyer (lender, insurer, employer) cannot directly observe the seller's (borrower, customer, worker) private type.