Auction (Economics)

An auction is a way of setting a price and allocating an item by inviting competing bids under rules announced in advance. The seller, or in a procurement auction the buyer, does not fix a price; instead, the bids reveal what participants are willing to pay. Auctions are used to sell art, houses, livestock, fish, government debt, radio spectrum, electricity, oil leases and online advertising space, and they underpin the opening and closing prices on stock exchanges.

Auction theory is a branch of game theory that studies how different formats shape bidding strategies, prices and efficiency, especially when bidders hold private information. It produced several Nobel prizes: William Vickrey, whose 1961 paper founded the field, shared the 1996 prize for work on incentives under asymmetric information, and Paul Milgrom and Robert Wilson received the 2020 prize for improvements to auction theory and the invention of new auction formats. Auctions are closely related to other price discovery mechanisms, such as order books and negotiation.

Suppose several people want the last ticket to a sold-out concert and the owner does not know what it is worth to them. Rather than guessing a price, the owner asks them to bid. The person who values it most ends up with it, and the price reflects how much the competition was willing to pay.

The rules matter a great deal. Bidding out loud, sealed envelopes, starting high and coming down, or paying the second-highest bid instead of your own all change how people behave. Designing those rules well can raise more money and put goods in the hands of those who value them most.

• English auction. An open ascending auction in which bidders raise the price until only one remains, common in art and property sales.
• Dutch auction. An open descending auction in which the price starts high and falls until someone accepts, used in flower markets and, in modified form, in some share sales; see Dutch auction.
• First-price sealed-bid auction. Each bidder submits one hidden bid, and the highest bidder pays what they bid; common in government procurement.
• Second-price sealed-bid (Vickrey) auction. The highest bidder wins but pays the second-highest bid.
• Multi-unit auctions. When many identical units are sold, a uniform-price auction charges every winner the same clearing price, while a discriminatory auction charges each winner its own bid.
• Double and call auctions. Buyers and sellers both submit orders, which are matched at a single price, as in the batch auctions that open and close trading on many a stock exchange.

In a second-price auction, bidding your true value is a dominant strategy: bidding more risks paying above your value, and bidding less only risks losing an item you would have bought profitably. In a first-price auction, bidders shade their bids below their values. With $n$ bidders whose private values are independent and evenly spread between zero and a maximum, the equilibrium bid is:

• $b$ is the bid submitted.
• $n$ is the number of bidders.
• $v$ is the bidder's own value for the item.

With four bidders, a bidder who values the item at 80 bids $3 \div 4 \times 80 = 60$. With more bidders, competition pushes bids closer to values. A central result, the revenue equivalence theorem developed by Vickrey and later by Roger Myerson and others, shows that under such idealised conditions the standard formats yield the same expected revenue. This is a Nash equilibrium result that breaks down when bidders are risk-averse, values are linked, or bidders collude.

When an item has a common value that no one knows exactly, such as an oil field, the winner is often the bidder who most overestimated it. This "winner's curse", documented by oil engineers in the early 1970s, is a classic case of asymmetric information. Rational bidders bid more cautiously to allow for it, but experiments find many do not, a finding taken up in behavioral economics.

• Government debt. Treasuries sell bills, notes and bonds at auction. Since 1998 the US Treasury has used a single-price (uniform) format for all its marketable Treasury securities, with primary dealers obliged to bid. Most other issuers of government bonds also auction them.
• Central bank operations. Central banks use auctions to supply or absorb liquidity in open market operations.
• Share sales. Most IPOs use book-building, but some, such as Google's in 2004, used an auction to set the price.
• Spectrum. The US Federal Communications Commission began spectrum auctions in 1994 using a simultaneous multiple-round format shaped by Milgrom and Wilson. The UK's 2000 auction of third-generation mobile licences raised about 22.5 billion pounds.
• Online advertising. Search engines and ad exchanges run billions of automated auctions a day to place ads, using variants of second-price and, increasingly, first-price rules.

Auctions can fail when bidders collude, forming a bidding ring or cartel to keep prices low; when too few bidders take part; or when the rules let strong bidders deter rivals. Some auctions that were poorly designed raised far less than expected. Designers must also balance revenue against efficiency: a government selling licences may care more about placing them with firms that will use them well, a Pareto efficient outcome, than about the highest price. Online auction platforms add a further issue, since buyers and sellers who never meet must rely on reputation systems and trust for the deal to complete.

• Nobel Prize: The Sveriges Riksbank Prize in Economic Sciences 2020
• Federal Communications Commission