Through our life as an economics major in undergraduate school, for three years we are repeatedly bombarded with consumer and producer theory, game theory, and general equilibrium theory. It is not until we are very familiar with these different topics, do we then come across what is, in my opinion, one of the most interesting topics in microeconomics. Auction theory and mechanism design.
The link between microeconomics and an auction may not be crystal clear, as it seems to be the case for consumer theory, where we study preferences and consumption. However, once you get thinking about it, auctions are exactly the setting economists care deeply about! How interesting is it for an economist to look at a situation where a seller is trying to sell some goods with multiple buyers implicitly competing with each other to obtain the goods? What interesting dynamics will reveal itself if we take a close, theoretical look at auctions? Let’s begin our exploration here.
Auction theory is closely related to game theory. An auction can be basically seen as a game, and as in game theory, the fun thing about auction theory is we can think about it in a heuristic manner. Of course, in academic research theoretical rigor is expected and necessary, however it is also the case that we can have a casual conversation about auctions and understand the basics of the mechanisms behind different auctions.
Firstly, let’s consider the type of auction we are all very familiar with. The open outcry auction, in this auction the price starts low and the auctioneer will continuously raise the price. As the price increases each bidder decides when to drop out, and once you drop out you cannot re-enter and the winner is the last person remaining in the auction and he pays the price at which the last person dropped out at. In this very common auction, how should bidders behave?
Let’s imagine you are sitting in an auction for a Vincent Van Gogh’s Starry Night. Other potential buyers are sitting around you looking anxious to own this great work of a painter who defines a generation, they all look rather more informed than yourself. However, you know one thing for sure. You like this painting A LOT and value it at a $120 million dollars.
The auctioneer on the podium begins the rapid firing of numbers into the audience. In the midst of all this turmoil you must decide when to drop out. Despite all the uncertainty revolving around the buyers you are competing against, it turns out that it is a weakly dominant strategy for you to simply drop out when the price reaches your private valuation of the painting.
Trivially, you wouldn’t want to drop out before the price reaches your private valuation, because then you are throwing away an opportunity to win the object for a payoff of zero, i.e. going home empty handed. It is also obvious you wouldn’t want to drop out after the price overshoots your private valuation. If you chose to do this, you may end up winning the auction but you will be paying more than how much you actually value the painting. Hence, it turns out that dropping out exactly when the price reaches your own private value of the good, is the weakly dominant strategy!
This is the attractive feature of an open outcry auction and it stems from the fact that your decision to drop out cannot really affect the price you will end up paying for the good (as you pay the price of when the second to last bidder drops out); it is a mechanism where the agents acting to maximize their payoff will choose to truthfully reveal their valuations. This feature is commonly sought after when economists are thinking about mechanism design problems and in my next article, we will explore other interesting features that surface when we really think about auctions.