Auction theory

From Wikipedia, the free encyclopedia

Auction theory is an applied branch of game theory which deals with how people act in auctions. There are many possible designs (or sets of rules) for an auction and typical issues studied by auction theorists include the efficiency of a given auction design, optimal and equilibrium bidding strategies, and revenue comparrison. Auction theory is also used as a tool to inform the design of real-world auctions; most notably auctions for the privatisation of public-sector companies or the sale of licenses for use of the electromagnetic spectrum.

1 Types of auction
2 Theoretical results
3 References
4 Further reading

[edit] Types of auction

There are traditionally four types of auction that are used for the allocation of a single item:

First-price sealed-bid auctions in which bidders place their bid in a sealed envelope and simultaneously hand them to the auctioneer. The envelopes are opened and the individual with the highest bid wins, paying a price equal to the exact amount that he or she bid.
Second-price sealed-bid auctions (Vickrey auctions) in which bidders place their bid in a sealed envelope and simultaneously hand them to the auctioneer. The envelopes are opened and the individual with the highest bid wins, paying a price equal to the exact amount of the second highest bid.
Open Ascending-bid auctions (English auctions) in which the price is steadily raised by the auctioneer with bidders dropping out once the price becomes too high. This continues until there remains only one bidder who wins the auction at the current price.
Open Descending-bid auctions (Dutch auctions) in which the price starts at a level sufficiently high to deter all bidders and is progressively lowered until a bidder indicates that he is prepared to buy at the current price. He or she wins the auction and pays the price at which they bid.

Most auction theory revolves around these four "standard" auction types. However, other auction types have also received some academic study, such as:

All Pay Auctions in which bidders place their bid in a sealed envelope and simultaneously hand them to the auctioneer. The envelopes are opened and the individual with the highest bid wins, paying a price equal to the exact amount that he or she bid. All losing bidders are also required to make a payment to the auctioneer equal to their own bid in an all-pay auction. This auction format is non-standard, but can be used to understand things such as election campaigns (in which bids can be interpreted as campaign spending) or queueing for a scarce commodity (in which your bid is the amount of time for which you are prepared to queue).
Lowest unique price auctions
Many homogenous item auctions
Simultaneous multiple-round auctions

[edit] Theoretical results

One of the major findings of Auction Theory is the Revenue Equivalence Theorem which states that under certain (reasonable) assumptions these auctions forms will lead to the same revenue for the seller.