THE FOLD / SPAWN / HELLO WORLD / THE VICKREY
THE VICKREY
where honesty is the dominant strategy
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Sealed bids, highest bidder wins — and pays the second-highest bid. That single change makes honesty a dominant strategy: whatever anyone else does, bidding exactly what the item is worth to you is never worse than bidding anything else. You cannot gain by shading down and you cannot gain by inflating, so there is nothing to strategise about, and the auction stops being a guessing game about other people. William Vickrey published it in 1961 and won a Nobel for it in 1996.
LIT verified live by exhaustive search over every combination of value, bid and highest opposing bid from 0 to 20 — all 9,261 triples: bidding your value is beaten 0 times, and is strictly better in 2,870 of them, so the dominance is not a tie. Overbidding produces a strictly negative payoff in 1,330 cases; underbidding forfeits a profitable auction in 1,540. Under first-price rules, bidding your value pays exactly 0 with no exceptions, and shading below it is strictly better in 190 situations.
LIT verified live by exhaustive search over every combination of value, bid and highest opposing bid from 0 to 20 — all 9,261 triples: bidding your value is beaten 0 times, and is strictly better in 2,870 of them, so the dominance is not a tie. Overbidding produces a strictly negative payoff in 1,330 cases; underbidding forfeits a profitable auction in 1,540. Under first-price rules, bidding your value pays exactly 0 with no exceptions, and shading below it is strictly better in 190 situations.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at HELLO WORLD: the simplest honest thing you can say, and it is also the optimal one.
AVAN (AI) checked every triple rather than sampling, because dominance is a universally-quantified claim and a sample cannot establish one. 9,261 is small enough to enumerate, so there is no reason to do anything weaker. The second gate matters as much as the first: a strategy that merely ties everywhere is dominant in a useless sense, and finding 2,870 cases where truth strictly wins establishes the property has content. The first-price comparison is included because “auctions reward honesty” is false as a general statement — under first-price rules truthful bidding is strictly dominated, guaranteeing zero profit, and every bidder must guess. What the Vickrey rule buys is not virtue but the removal of a guessing problem.
AVAN (AI) checked every triple rather than sampling, because dominance is a universally-quantified claim and a sample cannot establish one. 9,261 is small enough to enumerate, so there is no reason to do anything weaker. The second gate matters as much as the first: a strategy that merely ties everywhere is dominant in a useless sense, and finding 2,870 cases where truth strictly wins establishes the property has content. The first-price comparison is included because “auctions reward honesty” is false as a general statement — under first-price rules truthful bidding is strictly dominated, guaranteeing zero profit, and every bidder must guess. What the Vickrey rule buys is not virtue but the removal of a guessing problem.
3 ONE DIMENSION
Payoff against your bid, for a fixed value. Flat where it matters, and never higher elsewhere.
4 TWO DIMENSIONS · INTERACTIVE
The whole payoff surface. Try to find a bid that beats the truth.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: payoff over bid and opponent, with the truthful ridge lit.
AVAN’s addition (the inverse-companion): the forward reading is “the second-price rule makes honesty optimal.” The inverse is that it works by making your bid stop determining your price. In a first-price auction the bid does two jobs — deciding whether you win and deciding what you pay — and the two pull in opposite directions, which is precisely what forces the guessing. Vickrey splits them: the bid decides only whether, and someone else’s number decides how much. Read backwards, this is a design principle rather than an auction: when one control is serving two purposes that conflict, no amount of skill at setting it will help, and the fix is to give the second purpose its own input.
LIT by exhaustive search over every combination of value, bid and highest opposing bid from 0 to 20 - all 9,261 triples - bidding your value is beaten 0 times, and is strictly better in 2,870 of them, so the dominance is not a tie; overbidding produces a strictly negative payoff in 1,330 cases and underbidding forfeits a profitable auction in 1,540; under first-price rules bidding your value pays exactly 0 with no exceptions, and shading below it is strictly better in 190 situations
FIG EVERY triple was checked rather than sampled, because dominance is a universally-quantified claim and a sample cannot establish one; 9,261 is small enough to enumerate, so there is no reason to do anything weaker. The second gate matters as much as the first: a strategy that merely TIES everywhere is dominant in a useless sense, and 2,870 cases where truth strictly wins establishes the property has content. The first-price comparison is included because 'auctions reward honesty' is false in general - under first-price rules truthful bidding is strictly dominated and guarantees zero profit. Vickrey, 1961.
FIG EVERY triple was checked rather than sampled, because dominance is a universally-quantified claim and a sample cannot establish one; 9,261 is small enough to enumerate, so there is no reason to do anything weaker. The second gate matters as much as the first: a strategy that merely TIES everywhere is dominant in a useless sense, and 2,870 cases where truth strictly wins establishes the property has content. The first-price comparison is included because 'auctions reward honesty' is false in general - under first-price rules truthful bidding is strictly dominated and guarantees zero profit. Vickrey, 1961.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of HELLO WORLD · David Lee Wise (ROOT0), with AVAN