THE VICKREY AUCTION — a dart

THE VICKREY AUCTION win at your bid, pay the next one

A sealed-bid auction with a twist: the highest bidder wins but pays only the second-highest bid. The magic is that this makes honesty a dominant strategy — you can never do better than bidding your true value, whatever anyone else does. Over-bid and you risk paying more than it is worth; under-bid and you only risk losing a good deal. Vickrey won the 1996 Nobel for it; its cousin runs the ad auctions of the web.

THE TECHNIQUE winner = highest; price = second-highest

The demo runs a second-price auction and shows truthful bidding is weakly dominant: live demo

HISTORY & CREDIT Vickrey · 1961

“Paying the second price loses the seller money.” — by the revenue-equivalence theorem it earns the same in expectation as a first-price auction, while inducing honest bids. cited

the rule · highest bid wins, pays the second-highest.
the incentive · your bid sets only whether you win, never what you pay — so bid your true value.
1961 · William Vickrey (Nobel 1996); the generalized second-price auction runs web advertising.

A price that makes honesty optimal. mechanism

RECOMMEND FOR I-13 truthfulness, on the compiler

On i-13, bids [10,7,5]: winner 0 pays 7, utility 3; under-bidding only risks losing (utility 0):

$ i13 run gm_vickrey-auction.i13 RUN OK · 65 step(s) winner_is_0 = 1 price = 7 util_truth = 3 util_underbid = 0 truthful_ge = 1 -- honesty weakly dominant

Recommend as a NULL — incentive design + a theorem (B39/B41). Winner and price are pinned functions of the bids; strategy-proofness is a proved property, not a same-function difference (and it reasons about an adversary’s incentives, B41). NULL — win at your bid, pay the next.