Does a second-price auction cure the winner's curse?

Question

Ten bidders value a common prize worth V; each estimate is V plus noise uniform on [-10, +10]. Now the auction is second-price (Vickrey): the highest bidder wins but pays the second-highest bid. Everyone bids their own estimate. Does paying the runner-up's bid remove the winner's curse? Quantify the winner's expected overpayment.

Accepted Answer

In a private-value Vickrey auction, bidding your true value is optimal and there is no curse. But this is a common-value auction, and the curse survives, because the price you pay depends on someone else's noisy estimate, and conditional on winning, that runner-up estimate is also biased upward. The relevant order statistics. For n i.i.d. Uniform[-a, a] draws, the expected value of the r-th largest is E[X{(r)}] = a\,\frac{n - 2r + 1}{n + 1}. The largest (r = 1) is a\frac{n-1}{n+1}; the second largest (r = 2) is a\frac{n-3}{n+1}. First-price benchmark. If the winner paid their own bid, the exp…

Does a second-price auction cure the winner's curse?

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