Swoopo.com has been called “the crack cocaine of auction sites.” Numerous bloggers have commented on its “penny auction” format wherein each successive bid has an immediate cost to the bidder (whether or not that bidder is the eventual winner) and also raises the final price by a penny. The anecdotal evidence is that, while sometimes auctions close at bargain prices, often the total cost to the winning bidder far exceeds the market price of the good up for sale. The usual diagnosis is that Swoopo bidders fall prey to sunk-cost fallacies: they keep bidding in a misguided attempt to recoup their (sunk) losses.

Do the high prices necessarily mean that penny auctions are a bad deal? And do the outcomes necessarily reveal that Swoopo bidders are irrational in some way? Toomas Hinnosaar has done an equilibrium analysis of penny auctions and related formats and he has shown that the huge volatility in prices is in fact implied by fully rational bidders who are not prone to any sunk-cost fallacy. In fact, it is precisely the sunk nature of swoopo bidding costs that leads a rational bidder to ignore them and to continue bidding if there remains a good chance of winning.

This effect is most dramatic in “free” auctions where the final price of the good is fixed (say at zero, why not?) Then bidding resembles a pure war of attrition: every bid costs a penny and whoever is the last standing gets the good for free. Losers go home with many fewer pennies. (By contrast to a war of attrition, you can sit on the sidelines as long as you want and jump in on the bidding at any time.) Toomas shows that when rational bidders bid according to equilibrium strategies in free auctions, the auction ends with positive probability at any point between zero bids and infinitely many bids.

So the volatility is exactly what you would expect from fully rational bidders. However, Toomas shows that there is a smoking gun in the data that shows that real-world swoopo bidders are not the fully rational players in his model. In any equilibrium, sellers cannot be making positive profits otherwise bidders are making losses on average. Rational bidders would not enter a competition which gives them losses on average.

In the following graph you will see the actual distribution of seller profits from penny auctions and free auctions. The volatility matches the model very well but the average profit margin (as a percentage of the object’s value) is clearly positive in both cases. This could not happen in equilibrium.