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The Winner's Curse

A common-value auction is one where the thing being sold is worth the same to everyone, but nobody knows what that is. Oil leases, illiquid bonds, a block of shares, a contract nobody has priced in a week.

Each bidder forms an estimate. Suppose the estimates are unbiased, meaning nobody is systematically high or low. It feels as though bidding your estimate must therefore break even.

It does not, and the reason is a conditioning error.

Winning is information

You do not win a random auction. You win the ones where your estimate was the highest in the room. Conditioning on having won, your estimate is not a draw from the unbiased distribution any more, it is a draw from the top of it.

The curse, stated
E[V∣your estimate, you won]<E[V∣your estimate]E[V \mid \text{your estimate}, \text{ you won}] < E[V \mid \text{your estimate}]

Winning is evidence that you were optimistic, and any bid that ignores this loses money on average despite being based on an unbiased estimate.

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