One-Shot Bidding

You’re at a used car auction. Heart racing. Should you bid early to signal confidence, or wait and snipe? Shade 10% below your number, or 20%? You rehearse three different strategies on the drive over.

Then the car ends up selling for a hundred bucks more than your cap. What else did you expect? With enough bidders who’ve done the same homework, the winning bid was guaranteed to converge to what the car is worth. All that strategy for nothing.

That’s Google Ads

An entire industry agonizes over bidding strategy. Target ROAS, manual CPC, bid adjustments by device and time of day. Google built Smart Bidding, Meta built Advantage+, and agencies built careers around managing them.

In a competitive market with enough advertisers, the winning bid converges to the advertiser’s true value. Expected surplus approaches zero. Bidding complexity is pure friction.

Manufactured

Google’s Generalized Second-Price auction isn’t truthful. Edelman, Ostrovsky & Schwarz (2007) proved that GSP has no dominant strategy. Your optimal bid depends on what everyone else bids, and you can’t see their bids. First-price auctions, which Google switched to in 2019 for display, aren’t truthful either. You have to shade your bid below your true value, but by how much depends on the competition you can’t observe.

Smart Bidding is the fake solution to the fake problem. Google dug the pothole and sells you wheel alignment. Advertisers can’t leave because years of optimizations lock them in, huddled around the keyword fountain for a sip.

Vickrey, 1961

Vickrey (1961) solved this sixty-five years ago. In a second-price sealed-bid auction, the dominant strategy is to bid your true value. You never overpay because you pay the second-highest bid. You never underbid because shading can only lose you auctions you would have won profitably. Honesty is optimal.

Clarke (1971) and Groves (1973) generalized this to multiple items: the VCG mechanism. Each winner pays the externality they impose on everyone else. Total value is maximized, truthful reporting is dominant, and the whole thing resolves in one pass.

Contrast the cost:

The computational waste is fixing a strategic complexity that nobody asked for.

Already Solved

Academia has known this for decades. Vickrey got the Nobel in 1996. Milgrom and Wilson got it in 2020 for practical auction design. Lahaie & Lubin (2025) closed the last gap: the allocation problem is a linear program, the LP dual gives the prices, and VCG is computable even for multi-item auctions. Lahaie works at Google Research. Google didn’t use it.

Three Numbers

In a power-diagram auction with VCG payments, an advertiser declares three things:

1. Center: an embedding of who their customer is
2. Sigma: how broad or narrow their reach should be
3. Bid: what a conversion is worth to them

Drag the query dot. The Climbing PT’s max bid is $8, but she never pays that. The price is always what the runner-up was worth. Move the query to the left, and see the price drop. This reflects how much less likely the customers there will convert. Move it toward the Sports PT and they take over. The customer is worth more to them in their turf.

That’s the whole job. The publisher sets a relevance threshold τ to filter bad matches. The scoring function picks the winner. VCG sets the price. No optimizer. No consultant. The advertiser just answers three business questions and the auction handles the rest. The simulation shows what happens when it does: specialists win the queries they’re best at, generalists stop overpaying, and the keyword tax disappears.

How do I set my bid?

Conversion rate times revenue per conversion. If 3% of clicks become customers worth $200 each, bid $6. You’ll always pay less anyway.

One-shot bidding. Report your value and let the mechanism do the rest. If your auction requires a PhD in game theory to bid optimally, the auction is the bug.

Written with Claude Opus 4.6 via Claude Code. I directed the argument; Claude researched prior art and drafted prose.

Part of the Vector Space series.