First-Price Auction
First-Price Sealed-Bid Auction · Also known as: FPSB, Sealed-Bid Auction, Bid-Equal-Price Auction
A first-price auction is a sealed-bid mechanism where all participants submit bids simultaneously without knowing others' bids. The highest bidder wins and pays their own bid (the price they offered). Systematically analyzed by William Vickrey in 1961, first-price auctions require bidders to balance between winning and profit, leading to strategic underbidding relative to true valuations in equilibrium.
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When to use it
Use first-price auctions when the auctioneer wants high revenue and simplicity. Widely used in procurement (construction, government contracts), art and antiques, and real estate. Suitable when bidders have independent private valuations and a single item is being sold. First-price is often preferred when the auctioneer values revenue over transparency, as it typically yields higher prices than second-price auctions in practice.
Strengths & limitations
- High revenue: Strategic underbidding reduces payments less than second-price auctions
- Simple mechanism: easy to understand and implement; winner pays bid
- Practical: widely used in real-world auctions and government procurement
- Robust to collusion: difficult for bidders to coordinate on shill bids without losing profit
- Non-truthful: bidders shade bids below valuations, leading to inefficient allocations in some cases
- Strategic complexity: bidders must estimate the distribution of competitors' valuations
- Vulnerability to bid shaving: small reductions in bid can prevent collusion and increase revenue
- Weaker transparency: no guarantee of revenue equivalence with second-price across all distributions
Frequently asked
Why do bidders shade (reduce) their bids in first-price auctions?
Because you pay your own bid if you win, you must balance winning probability against profit margin. Bidding your true valuation would eliminate profit. Optimal bid shading depends on competitors' expected bids, which depends on their valuations and bidding strategy.
Is a first-price auction revenue-equivalent to a second-price auction?
Revenue equivalence holds when bidders have independent private valuations drawn from the same distribution. However, under affiliated valuations (common value components), first-price can yield higher revenue because bidders shade less aggressively.
How does the number of bidders affect equilibrium bidding in first-price auctions?
As the number of bidders increases, each bidder's shade decreases, and bid functions converge to true valuations. With few bidders, shade is more aggressive. This is because increased competition reduces the bidder's advantage from shading.
Sources
- Vickrey, W. (1961). Counterspeculation, auctions, and competitive sealed bids. The Journal of Finance, 16(1), 8-37. DOI: 10.1111/j.1540-6261.1961.tb02789.x ↗
- Krishna, V. (2009). Auction Theory (Second Edition). Academic Press. link ↗
How to cite this page
ScholarGate. (2026, June 3). First-Price Sealed-Bid Auction. ScholarGate. https://scholargate.app/en/game-theory/first-price-auction
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