What is Auction Theory?

Auctions are Everywhere

Auctions are so common nowadays that I bet most of you have participated in auctions in the last year. Even if you haven’t, auctions have probably impacted your life indirectly. The cost of the road you drive on, the price of your airline ticket, and where your medical friend goes to residency, are all areas that auctions have a big impact.

Here is a sampling of common auctions:

• eBay auctions
• Google Adwords
• Craigslist
• Residency match
• Dating matches
• Donor matches
• Job offers
• FCC spectrum auctions
• Emissions markets
• Public construction projects

Auction theory provides a systematic way to analyze all of these diverse projects. I’ll go into more details in future articles, but for today I want to give a broad overview of the field.

What is an auction?

An auction is a special market that assigns goods to the highest bidders. In general, there are three main components to an auction:

• Bidders that demand a product
• Sellers supplying a product
• An auctioneer overseeing the market (usually for a fee)

A common auction site like eBay readily illustrates the role of each player:

• Consumers are the bidders and demand items
• Product listers are the sellers that offer products
• eBay acts as the auctioneer and charges a listing fee to sellers

As you might guess, the types of bidders, the types of sellers, and the precise auction rules can lead to vastly different outcomes. Some auctions are more favorable to bidders, some to sellers, and some to auctioneers. And different auctions afford different player strategies.

When did auction theory begin?

It all began with women. Well, selling women that is.

Econport provides a brief history of auctions:

The history of auctions extends back to 500 B.C. when Herodotus reported the use of an auction. These auctions were for the purpose of selling women under the condition that they be married following purchase. Reports indicate that less attractive women were sold with monetary compensation given to the bidder.

Modern auctions are more sophisticated, and laws prohibit auctioning off certain items (you can’t sell organs on eBay).

Although auctions have been used since antiquity, they were first analyzed systematically in 1961 using the tools of game theory. This is the year William Vickrey authored the influential paper “Counterspeculation, auctions and competitive sealed tenders” in the Journal of Finance. Vickrey demonstrated equilibria to several auctions and also proved how seemingly different auctions were mathematically equivalent and can produce equivalent seller revenue. Vickrey won the Nobel Prize in Economics in 1996.

The modern era of auction theory can be dated to 1993-1994 with the revolutionary FCC spectrum auctions in America, according to Paul Milgrom in Putting Auction Theory to Work. The move created much publicity for auction theory, and many auctions have occurred since, including timber auctions, emissions auctions, and asset auctions.

What are some important concepts from auction theory?

Price discovery

Let’s say you have a rare antique. How much should you sell it for? If you use traditional retailing you need to fix a price. In an auction, however, the selling price can be “discovered” by collecting bids and awarding the item to the highest bidder.

Bidding strategy

How much you’re willing to bid depends on the value of the good to you (and possibly to others), what you think others will bid, and the exact rule converting bids into payments. Small auction rules often create unintended consequences. While eBay and Amazon both have similar auction markets, a specific rule on eBay has led to “sniping” behavior, which research shows is a very good strategy.

Winner’s curse

There are some games where the winners always seem to be losers. Consider how many sports all-stars seem to get overpaid in lackluster off-seasons. The team that has the highest valuation of the star often tends to overestimate values. Before you bid, it would be a good idea to know if the winner’s curse might apply to your auction.

Collusion

Buyers and sellers can cooperate, or collude, to take advantage of the market. If a seller on eBay lists three our four identical items separately, buyers could in theory cooperate to keep each item price low and avoid bidding wars. Conversely, sellers of a limited product can collude and keep high reserve prices to avoid price wars.

Future articles

Here are some topics I plan to cover in future articles.

• Winner’s curse
• Various types of auctions (first-price, sealed bid…)
• Selling on specific auctions (eBay, Amazon, Craig’s List…)
• The dollar auction game
• Matching auctions
• Revenue equivalence