Firstprice

A first-price auction, also called a first-price sealed-bid auction, is a sale format in which bidders submit confidential bids for a good or contract. The highest bid wins and the winner pays the amount they bid.

Bidders do not observe others' bids; the strategy is to bid below one’s own valuation to balance the chance of winning with the price paid. In equilibrium under common assumptions (independent private values, risk neutrality, symmetric bidders), bidding strategies shade bids: higher valuations lead to higher bids, but not equal to the value. For example, with n risk-neutral bidders and valuations uniformly distributed on [0,1], the symmetric equilibrium bid is b(v) = (n-1)/n * v.

Compared to a second-price sealed-bid auction, where the winner pays the second-highest bid, the first-price format incentivizes more aggressive bid shading and can lead to different revenue outcomes; the choice of format interacts with bidders’ risk preferences and the information structure of the contest.

Applications and variations of first-price auctions are widespread. They are used in single-item and multi-unit procurement, government tenders, and various online and offline marketplaces. Common variations include reserve prices, which set a minimum acceptable price, bidding increments, and rules for handling tied bids. In practice, outcomes depend on the distribution of bidders’ valuations, the number of participants, and any strategic considerations such as collusion or information asymmetries.

The concept is a central part of auction theory, often contrasted with English (open ascending) and second-price auctions. Under standard theoretical assumptions, different sealed-bid formats can yield similar expected revenue, though real-world results vary with risk, information, and reserves.