New Zealand, 1990. The government hires consulting firm NERA to design a radio spectrum auction. NERA recommends the Vickrey auction — a format whose theoretical foundations would earn a Nobel Prize six years later. Expected revenue: NZ$250 million. Actual revenue: NZ$36 million. One bidder offered NZ$100,000 and paid NZ$6. Another bid NZ$7 million and paid NZ$5,000.
One wrong choice of auction format cost the treasury NZ$214 million.
In 2019, Google changed the auction format for the $48 billion programmatic advertising market. In 2021, the FCC raised $81 billion in a C-band spectrum auction — a world record. The EU ETS has generated €245 billion from auctioning the right to pollute since 2013. In every case, it wasn’t the good that determined the price — the auction rules determined the price.
Four Basic Auctions
Every auction in the world is a combination of two variables: open or sealed bids, and whether the winner pays their own price or someone else’s.
First-Price (pay your bid)
Dutch (open, descending)Price falls from ceiling. First to say "stop" wins and pays current price. Strategy: wait longer = cheaper, but risk losing.
Sealed first-price (closed)Tenders, government procurement, programmatic ads since 2019. All submit bids in sealed envelopes. Highest wins. Strategy: bid shading — bid below true value.
Second-Price (pay 2nd bid)
English (open, ascending)Christie's, Sotheby's. Price rises. Last bidder standing wins and pays just above second-highest. Strategy: bid up to your true valuation, no higher.
Vickrey (sealed second-price)Nobel Prize 1996. Highest bid wins, but pays second price. eBay's proxy bidding. Dominant strategy: bid exactly your true valuation.
Strategic equivalence:
Dutch ≈ Sealed first-price (same strategy, different pacing). English ≈ Vickrey (same outcome — winner pays ~second valuation). Two pairs that look different but are strategically identical.
How It Works: One Item, Three Prices
Three bidders value a painting at $100, $80, and $50. What happens under different rules?
First-Price Sealed
Optimal bid with n=3: b(v) = v × ⅔
- Bidder A: values $100, bids $67 — wins
- Bidder B: values $80, bids $53
- Bidder C: values $50, bids $33
- Seller receives: $67
Vickrey (Second-Price)
Dominant strategy: bid your true value
- Bidder A: values $100, bids $100 — wins
- Bidder B: values $80, bids $80
- Bidder C: values $50, bids $50
- Seller receives: $80 (second bid)
English (Open Ascending)
Price rises until one bidder remains
- C drops out at $50
- B drops out at $80
- A wins, pays $81 (one step above B)
- Seller receives: ≈$80
Bidding Formulas
Second-Price (Vickrey)
b(v) = v. Bid your true value. Always. Dominant strategy — independent of number of participants and their behavior.
b(v) = v
First-Price (Sealed)
b(v) = v × (n−1)/n. With 2 bidders: shade 50%. With 10: shade 10%. More competition → more aggressive bids.
b = v·(n−1)/n
Bid shading by number of participants (value = $100, first-price):
Revenue Equivalence Theorem
E[RevenueFP] = E[RevenueSP] = (n−1)/(n+1)
With n bidders drawing values from U[0,1], the expected seller revenue is identical across all four formats. The key word is expected: in any single auction prices differ, but across many they converge. Vickrey 1961 (2 bidders), Riley & Samuelson 1981 (general case) → Nobel Prize 1996.
Conditions: independent private values, risk neutrality, symmetric bidders, no collusion. In reality, every condition is violated — making format choice a critical decision.
Independent private values
If holds: all formats equal
- If violated: English yields more (less winner's curse)
- Example: oil exploration — correlated values
Risk neutrality
If holds: RE works
- If violated: first-price yields more (risk-averse bidders shade less)
- Example: government contracts
Symmetric bidders
If holds: RE works
- If violated: strong bidder shades more; weak overbids
- Example: NZ 1990 — incumbent vs newcomer
No collusion
If holds: RE works
- If violated: second-price → floor manipulation; English → ring bidding
- Example: header bidding SSPs
The New Zealand Disaster
NZ$250M
expected revenue
NZ$36M
actual revenue
86%
revenue lost
Specific lots:
| Lot | Bid | Paid | Discount |
|---|---|---|---|
| Radio frequency license | NZ$100,000 | NZ$6 | 99.994% |
| Radio frequency license | NZ$7,000,000 | NZ$5,000 | 99.93% |
| National cellular license | NZ$101,000,000 | NZ$11,000,000 | 89.1% |
| Sky Network TV, Lot 1 | NZ$2,371,000 | NZ$401,000 | 83.1% |
Three design errors:
(1) No minimum price (reserve price) — you could bid $6. (2) Sold identical licenses through separate Vickrey auctions instead of a unified uniform-price auction. (3) Asymmetric participants (incumbents vs newcomers) — revenue equivalence breaks down.
Comprehensive Format Comparison
English (ascending)
- Strategy: bid up to true value
- Pays: ≈ 2nd valuation
- Info: high — see other bids
- Speed: slow (minutes–hours)
- Collusion resistance: low
- Winner's curse: less dangerous
Dutch (descending)
- Strategy: bid shading
- Pays: own bid
- Info: low — one price
- Speed: very fast
- Collusion resistance: high
- Winner's curse: dangerous
First-Price (sealed)
- Strategy: bid shading
- Pays: own bid
- Info: zero
- Speed: one round
- Collusion resistance: high
- Winner's curse: most dangerous
Vickrey (second-price)
- Strategy: b(v) = v (dominant)
- Pays: 2nd bid
- Info: medium — 2 prices
- Speed: one round
- Collusion resistance: medium
- Winner's curse: absent
Ad Auctions: 100 Milliseconds and $500 Billion
Advertising auctions are the most massive in history: trillions of auctions per day. Their 12-year evolution recapitulated the path auction theory traveled over 50 years.
2007
RTB and second-price auctions
Birth of programmatic: SSPs run real-time Vickrey auctions. Highest bidder wins and pays second price + $0.01. Truthful bidding — everyone bids their true value.
~2012
Waterfall: cascade of inefficiency
Publishers call ad networks sequentially: Google first, then rest. An $8 bid from the third SSP never beats the $5 price from the first — it's never seen. Loss: 20–40% of revenue.
2014–15
Header bidding: simultaneous auctions
Revolution. All SSPs receive bid requests simultaneously. Prebid.js (2015, open source) becomes the standard. 84% of top 10K US sites. RPM growth 30–40%. Sequential → simultaneous auction.
2017
Exchanges switch to first-price
OpenX, Rubicon Project and others drop second-price. Reason: in header bidding, second-price enables SSP floor-price manipulation. First-price is simpler and more transparent.
2019
Google Ad Manager → unified first-price
Google — the last major exchange. Eliminates "last look" privilege. Unified auction = one first price for all. Bid shading becomes mandatory. The $48B market shifts overnight.
2021
AdSense → first-price. Full circle.
The last second-price bastion in Google falls. Theory said second-price → truthful. Practice: first-price + bid shading. Bid shading can take up to 20% of publisher revenue.
Summary:
Ad industry traveled from Vickrey (2007) to first-price (2019) in 12 years — for the same reasons Vickrey described in 1961: when values correlate, bidders are asymmetric, and intermediaries exist, second-price creates manipulation opportunities. The theory wasn't wrong — the conditions of application were.
Auctions in Finance
Financial markets are auctions with different names. Treasury, IPO, buyback — the same mechanisms everywhere.
US Treasury Bills
Dutch / uniform-price auction
- Fed NY sells government bonds via Dutch auction
- Primary dealers bid with desired yield
- All winners pay a single price
Google IPO, 2004
Modified Dutch auction
- Investors specified price and volume
- Final price $85 — uniform for all
- First day: +18%. Goal: minimize underpricing
Stock Exchanges
Continuous double auction
- NYSE, NASDAQ — buyers and sellers bid simultaneously
- Trade on bid/ask intersection
- Billions of trades daily
EU ETS Carbon Market
Sealed uniform-price
- Weekly auctions on EEX exchange
- Average 2024 price: €65/tCO₂ (peak 2023: €100+)
- 599M allowances sold in 2024
Energy Markets
Uniform-price merit order
- EPEX SPOT (Europe), PJM (US): hourly bids
- Cheapest sources (solar, wind) first, then expensive (gas)
- Marginal price = last generator activated
FCC Spectrum Auctions
SMRA (Milgrom-Wilson design)
- C-band auction 2021 — world record
- Nobel Prize 2020 for auction design
- Simultaneous multiple round auction
Auctions in Technology
AWS Spot Instances
Up to 90% discount on idle EC2 capacity
- Since 2009: auction for unused compute
- In 2017 switched from pure auction to smoothed pricing
- Interruption: 30 sec – 2 min notice
Ethereum Gas (EIP-1559)
First-price → hybrid mechanism
- Pre-2021: pure first-price auction for block space
- Post-EIP-1559: base fee (algorithmic) + priority tip
- Significant reduction in fee volatility and waiting times
Domain Auctions
English auction + reserve price
- GoDaddy, NameJet, DropCatch for expired domains
- voice.com sold for $30M (2019)
- Premium domains via sealed-bid on Sedo/Afternic
Pattern:
The same evolution repeats everywhere. Start with a pure auction (AWS Spot 2009, Ethereum pre-1559, programmatic 2007). Over time, transition to a hybrid: auction mechanism + algorithmic pricing. Pure auctions are too volatile for production systems. Stability beats theoretical optimality.
Where Auctions Are Heading
AI Bidding Agents
Now → 2027
- ML algorithms already do bid shading (Google, TTD)
- Next: autonomous agents trading without humans
- Risk: algorithmic collusion without explicit agreement
Privacy-Preserving Auctions
Now → 2028
- Apple ATT, Privacy Sandbox, EU DSA — user data disappearing
- On-device bidding, federated auctions, contextual signals
Combinatorial Auctions
2025+
- FCC Incentive Auction (2017) — first major example
- NP-hard, solved with SAT-solvers
- Next: 5G/6G shared spectrum, multi-cloud procurement
Dynamic Mechanism Design
2026+
- Classical theory covers one-shot auctions
- Reality: billions of repeated auctions with learning participants
Real-Time Energy Markets
2025+
- P2P electricity auctions between households
- Pilots: Power Ledger (Australia), Sonnen (Germany)
Auctions → Automatic Markets
Long-term
- AWS Spot is no longer an auction — it's algorithmic pricing
- Pure auctions dissolve into dynamic pricing
- The foundation — auction theory — remains
Evolution: From Gavel to Algorithm
Pre-20th century
English, Dutch — minutes to hours
People in a room. Christie's (1766), Aalsmeer flower auction (1911).
1960–1990
Sealed-bid, Vickrey — days to weeks
Companies + governments. NZ Spectrum 1990, US Treasury auctions.
1994–2010
SMRA, combinatorial — weeks to months
Telecoms + regulators. FCC Auctions designed by Milgrom & Wilson (Nobel 2020).
2007–2019
RTB second → first-price — 100ms
DSP/SSP algorithms. Programmatic advertising, header bidding revolution.
2020+
ML bid agents + hybrid — microseconds
AI vs AI. Auto-bidding, Spot pricing, EIP-1559. Auction theory as invisible OS.
One Lesson
Rules determine behavior. Behavior determines price. Whoever designs the rules owns the market.
The same radio waves cost between $0.001 and $0.875 per MHz/pop — an 875× difference. The same ad generates 30–40% more or less revenue depending on the auction format. The same carbon costs €5 or €100 — depending on cap-and-trade rules.
An auction is not a gavel at Christie’s. It’s a model of any market with competition for a scarce resource.
AI Disclosure: Research conducted with Claude (Anthropic). Human editorial direction and domain expertise.