Auctions - a brief introduction

First things first: What are Auctions?

Bidding at a local auction is interrupted when the auctioneer’s clerk hands him a note. “A gentleman has lost a wallet containing $5,000 in cash,” says the auctioneer. “If it is returned, he will pay a reward of $1,000.” There is a moment of silence, then someone in the crowd shouts: “One thousand five hundred!”

There is a price for everything and auctions are designed to find the right price in situations of high information asymmetry between the seller and potential buyers.

Auctions are not a new idea. The Babylonians auctioned wives, the ancient Greeks auctioned mine concessions, and the Romans auctioned almost anything, from spoils of war to slaves. Today, auctions are the instrument of choice for a very high volume of economic transactions. Governments use auctions extensively to sell foreign exchange, bonds, rights to natural resources. We use them to sell houses, cars, art and antiques ^[1].

I will be introducing you to the four main types of auctions, real-world examples where these auctions are used and the dominant strategy for bidders to play:

Ascending-bid auctions (a.k.a. the Open or the English Auction)
Descending-bid auctions (a.k.a. the Dutch auction)
The First-Price sealed-bid auctions
The Second-Price sealed-bid auctions (a.k.a The Vickrey auction)

Ascending-Bid Auctions

Naming things is hard, but with auction names they sort of nailed it (well, some of the time, as we shall see). While often ascending-bid auctions get collectively referred to as the English Auction, there are a few variations, some of which are very creatively called: “The Japanese”, “The Swedish” and “The Candle” auctions.

Here is how the English auction works: the price is successively raised until only one bidder remains, and that bidder wins the item at the final price. The question now is: Who raises the price? In the English auction, the price is raised by the bidder.

Dominant Strategy

We’ve all seen that movie where they’re selling a famous painting, and the auctioneer says: “We start at $1.4 million”. Then comes the first bid, then a slightly higher one, then another one, and another one, … and finally, in the monotony of small increments, from the back of the room, usually in a deep hoarse voice, someone shouts: … $100 million.

Figure 1: Scene from the movie The Best Offer ^[2]

Everyone turns their head. No more bids. Sold.

Paintings are sold through what is commonly called an English auction. Going from $1.4 million to $100 million is what economists call jump bidding. That is increasing your bid more than asked for by the auctioneer. Jump bidding is a suboptimal strategy to play as a participant. In English auctions, the bidders raise the price. The dominant strategy here is for bidders to play with small incremental bids. The reason is very simple. By jump bidding you may be costing yourself money, because you do not know at what price others would have stopped bidding, and you could have ended paying a lower price.

Variations and examples

The Japanese Auction. Instead of bidders raising the selling price with their bids - it’s the auctioneer that sets an electronic increment of the price, which bidders either accept or not. If you don’t, you’re out and can no longer place a bid. When there is only one bidder accepting, the auction ends. This is the model used by most auction theorists.

The Swedish Auction. In most countries I am familiar with, selling a house usually goes like this: The house owner sets a preferred price and then negotiates with potential buyers. Not in Sweden. They like to auction their houses. Here’s the odd thing: bids are not binding. The winner, can choose to not pay. Ascending-bid auctions where bids are not binding, are called Swedish auctions.

The Candle Auction. Note that Candle in this variation is not meant metaphorically. The end of the auction is literally signaled by the flame of a candle going off. The reason: adding some uncertainty about the time the auction ends, to avoid last moment bids, and guarantee a higher price. This was quite in fashion a few centuries ago, when they had candles, you know.

Descending-bid Auctions

This is known by several names too, most notably as the Dutch auction. It is also sometimes referred to as the open-outcry descending-bid auction or the clock auction.

Here is how it works: The initial price set is very high. The auctioneer constantly lowers the price until the one bidder accepts it. As you may have noticed, this kind of auction only needs one bid to end. What if there is no bid? Usually there is a reserved price under which the object is not sold. What if there are several bids? This is good problem to have, but which can easily be mitigated by using some electronic system.

Note that in this type of auction the seller can end up selling at a price that is lower than the buyer may have been willing to pay. Before you starting thinking the Dutch are stupid, you should know that for some things, this way of auctioning makes sense.

Dominant Strategy

In this type of auction, the bidder’s true valuation of the thing being sold is very important. So let’s assume Alice’s true valuation of the thing being sold is $v$ . Bidding more than $v$ , is irrational because she ends up losing net value. If she bids exactly $v$ , she will neither gain nor lose net value. So the question is: How much should Alice bid?

We know that she would like to bid the smallest amount that will still allow her to win, but this amount must be less than $v$ . Let’s assume Bob is another bidder, and he decides to bid $y$ and $y < v$ . Ideally Alice would like to bid $y + ε$ , where $ε$ is the smallest increment possible, e.g. one cent).

But Alice does now know what others will bid, so what we have here is a Bayesian Game. The best shot at winning Alice, and other bidders have, is estimating the highest bid from competitors. Unfortunately, this is not easy even when there are only two bidders, so there is no dominant strategy.

Examples

Selling tulips. You may have heard about Tulip Mania ^[3]. When Ottoman traders brought tulips to Holland, the Dutch fell in love with them, especially with the Semper Augustus tulip.

What’s special about the Semper Augustus is that its color is caused by a virus, which makes its cultivation hard, and its supply scarce. To grow tulips, even normal ones, takes up to seven months. Supply was not keeping up with the demand, and prices surged. How Tulip Mania happened is very interesting, and it deserves its own post.

Back to the point, why did the Dutch auction make sense for selling tulips? The Dutch auction was invented to get traders in and out with what they wanted as quickly as possible and at a high price.

This kind of auction however, does not belong in history books. It is used to this day by some of the largest financial institutions for public offerings.

The First-Price Sealed-Bid Auction

Also known as a blind auction.

Here is how it works: The participants submit their sealed bids at the same time. This way, no one knows the bids placed by other participants. The highest submitted bid wins. This is different from the English auction where participants know the bids of other participants.

In a first-price sealed-bid auction, a big issue is privacy. Having information on participants and competing bids can drive the auction price down. In certain cases (when multiple units of the same something is being sold) it can also incentivize collusion, although luckily collusion is not a stable equilibrium as there are plenty of incentives to cheat.

Dominant Strategy

Strategically this is equivalent to a Dutch auction. There is no dominant strategy.

Examples

Government Contracts. Government and Organizations use blind auctions very often. Government contracts are almost exclusively always organized as blind auctions. In these cases, of course, the auctioneer is seeking a low price rather than a high price. Usually a maximum contract value is specified (reserved price), and the auction is opened. Participants try to outbid each other by submitting bids lower than the announced contract value.

Selling Dried Fish in Japan. Bidders deposit their bids in a box which is then handed to an auctioneer. After some agreed-upon time interval has expired, the auctioneer announces the winner.

Discriminatory Auction. What happens when you want to sell more than one unit of an item. Here bidders pay different prices for the same unit. Sealed bids have two components: price and quantity the bidder wants to buy at that price. Bids are then sorted from high to low, and the “asked” quantity of items per bid are awarded at the highest bid price until the supply is exhausted. The U.S. Treasury uses the discriminatory auction to sell most of the treasury bills, notes, and bonds that finance the national debt of the United States.

Here is a good summary of The First-Price sealed-bid auction theory ^[4].

The Second-Price Sealed-Bid

This is my favorite type of auction. In the second-price sealed-bid auction, each bidder independently submits a single bid, without seeing others’ bids, and the object is sold to the bidder who makes the highest bid. However, the price the winner pays is the second-highest bidder’s bid, or second price.

This auction is often called a Vickrey auction after Columbia University Professor William Vickrey, who wrote the seminal (1961) paper on auctions where he formalised the mechanics of Lerner’s vague suggestion of a counterspeculation agency, solving the issue of maintaining marginal conditions for efficient resource allocation in a situation of imperfect competition ^[5].

Dominant Strategy

The cool thing about this type of auction, is that the dominant strategy is for each bider to bid a price that reflects their true valuation of the thing being sold.

This is how you can reason about it: Alice is bidding to buy something in a Vickrey auction. Alice’s true valuation of the thing being sold is $v$ . Assume the highest competing bid is $p$ . If Alice bids $v$ and if $v > p$ , then Alice wins the auction, and earns $v - p$ . There is no other amount Alice could have bid for that would give her better earnings. What if $v < p$ ? Still, the best Alice could do is to bid $v$ as anything above that, to her means losing money. So bidding $v$ , the true valuation Alice has for the thing being sold, is the optimal strategy.

Because of this the second-price auction is also called a demand revealing mechanism.

Examples

Google AdWords. A famous application of the Second-Price Sealed-Bid auction is how advertisers bid on keywords in Google AdWords. In 2016 Google made $79.38 billion in revenues from ads.

Auctions: Theory and Practice by Paul Klemperer ↩︎
The Best Offer ↩︎
Tulipmania by Peter M. Garber ↩︎
First-Price sealed-bid Auctions ↩︎
Counterspeculation, Auctions and Competitive Sealed Tenders ↩︎