Unveiling Auction Theory

A comprehensive and simple guide to the field of auction theory

Image taken from Google

The year 2020 was a big year for applied economics. It was the year when two brilliant minds - Paul Milgrom and Robert B. Wilson were announced as the recipients of The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel or as most people know it, the Nobel prize in Economics¹. They were selected because of their contributions to the field of Auction Theory - an applied branch of Economics.

Compared to another applied branch of Economics such as Behavioral Economics, Auction Theory may be less popular among the non-economists. One reason might be because it is mathematically more rigorous. That being said, Auction Theory can actually be utilised to solve variety of real life problems. One example of the applications is in the electromagnetic market where various governments around the world utilise auction theory to sell electromagnetic waves to telecommunications firms. The result is quite astounding. The Federal Communication Commission (FCC) in the US for example, raised a whopping amount of $60 billion by applying Auction Theory²!

Aside from government agencies, some tech firms also incorporate Auction Theory into their business models. For example Google utilises Generalised second-price auction algorithm for their online advertising platform whereas Facebook uses Vickrey-Clarke-Groves auction. As you can see, Auction Theory is a very applicable field of Economics. Before we dive into these complicated version of auctions in the near future however, it might be worthwhile to spend some time understanding the fundamentals of auction theory which something we will explore in this article. A bonus content is also added at the very end of the article for the nerds out there :).

Auction Theory is a discipline that studies the behaviour of bidders in auctions for the purpose of achieving market equilibrium while at the same time avoiding market failure. The field is closely linked to game theory and economics of asymmetric information. There are two fundamental problems that auction theorists try to solve:

  1. How can we maximise the revenues of the sellers/auctioneers?
  2. How can we ensure the items fall into the hands of buyers/bidders that value them the most?

To put it simply, every auction theorist seeks to answer the following question:

“Is it possible to design a set of rules for auctions in such a way that it will benefit both the auctioneers and the bidders?”

In addition to the question, auction theorists also have to know the types of the auctions and the products. As far as products are concerned, there are two types:

  • Products with Independent Private Values (IPV)
  • Products with Common Values (CV)

A product with IPV means that each bidder knows exactly how much the product is worth to him and his valuation of the product will not be affected by others. A product with CV means that the value of the item is identical among bidders but each bidder has different degree of information about this value. In this situation, learning about how much information others have may lead to a change in your original valuation. These are however, the two extremities of the types of products. In real life scenarios, the products usually fall somewhere between these two opposite end. One example will be an art auction. Each bidder will have their own preferences about the piece of art. However, they will also care about how others value the art in case they want to re-auction the art in the future.

Aside from the types of the products, there are four fundamental types of auctions that we usually consider. A more complicated type of auction is usually a variation of these four. The four basic types are as follows:

  • English Auction
  • Dutch Auction
  • First-Price Sealed Bid Auction
  • Second-Price Sealed Bid Auction

The English Auction is the most commonly used auction. It is the type of auctions that one normally sees in a lot of movies where bidders try to outbid others by keep rising the bid price. It is also known as the ascending price auction. The Dutch Auction is the opposite of English Auction. In this type, the auctioneer will set up a starting price and then he/she will keep lowering the price until a bidder accepts the current price. It is also knows as the descending price auction. The First-Price Sealed Bid Auction is a type of auction where bidders will submit their bid in envelops and send them to the auctioneer. The auctioneer will then open these bids and allocate the product to the one with the highest bid and ask him/her to pay the winning bid. The Second-Price Sealed Bid Auction works in the same way. However, in this case, the winner will not pay its winning bid. The pay price will be the second-highest bid. This type of auction is also known as Vickrey Auction and is special among all types of auctions. It is special because of its wonderful property: the self-revelation principle.

Using game theoretic approach, we can prove that the bidders under Vickrey Auction will have incentives to reveal their true valuations of the products. In simpler words, bidders will not lie about how much they value the goods! Sounds like magic? It is. The downside of the Vickrey Auction is of course it needs specific conditions which is the reason why it is not widely applied in the industry. The good news is, a lot of improvements have been made. Google’s generalised second price auction algorithm and Facebook’s VCG for example are less restricting version of the Vickrey Auction. While the former does not strictly induce the self-revelation principle, the latter does! This opens up possibilities for Vickrey Auction to be more widely applied.

Here comes the interesting question. Okay, so we have these four types of auctions and two types of products. How will this help us in designing our auctions? How do we know which one of these is the most beneficial? While I want to give a firm and direct answer, I can’t. The reason is of course in real scenarios, there are multiple factors that we need to consider. In the spectrum auction for example, we need to consider bundling. Electromagnetic frequencies are not useful on their own. Most of the time they need to be combined/bundled before being auctioned. In light of this, the achievement of both Paul Milgrom and Robert B. Wilson in designing a set of rules that work for frequencies is indeed amazing and worthy of the prize!

It is however still useful to study the most fundamental scenario. In the field of Auction Theory, the most fundamental scenario has three benchmark assumptions:

  • The bidders are risk-neutral
  • The bidders have independent private values
  • The bidders are symmetric

Without going too deep into the assumptions and the mathematics, under this condition, it does not matter which auction type we choose! Each auction type will yield the same revenue for the sellers/auctioneers! This is called the Revenue Equivalence Theorem.

And thus our short journey into the field of auction theory comes to an end. Hopefully this has been an interesting read and spark your interest about auctions. For those of you who are interested in knowing more about the work of both Paul Milgrom and Robert B. Wilson, do click on the following link: https://www.nobelprize.org/prizes/economic-sciences/2020/press-release/.

Bonus content: https://albert14wibowo.medium.com/proving-the-mysterious-vickrey-auction-47cacb9c68d1

[1] I am quite reluctant to use Nobel prize in Economics because technically, there is no nobel prize in economics.

[2] The FCC also hired Paul Milgrom as a consultant

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