## Losing to win: Tullock auctions

In the typical auction systems – English, Dutch, first-price and second-price – the most logical course of action would be to bid your value (English and second-price auctions) or lower (Dutch and first-price auctions). In these auctions, the winner profits from getting an item at a price slightly less than his value. Since the price of the item was higher than the value of the other bidders, there is no ‘loss’ for the other bidders who do not have to pay. However, in a different auction format called the Tullock auction (a simple form of the all-pay auction), every bidder pays their bid regardless of whether they win or lose. Bidding in a Tullock auction is not like the typical auction – here, the logical way to act is to bid above your value. In Michael Munger’s podcast with Russ Roberts, Munger, professor of economics, public policy and political science at Duke University, explains the logic behind Tullock auctions and how they can make people bid at a loss.

Bidding at a loss sounds counterintuitive, but this is indeed the logical outcome of a Tullock auction. Munger illustrates this logic with an example from an experiment he runs in his class. He tells the class that he’s going to hold an auction to give away \$10. The highest bidder will win the money. The catch is that everyone has to pay their bid. To the class, that sounds wonderful – the professor is going to give away money almost for free. To get the whole \$10, one person might bid \$0. However, the next person may decide that in order to win the \$10, they will bid 1 cent and settle for a decent sum of \$9.99. The next person might bid 5 cents, and the next 7, and so on. In a common auction, the bid price would go up to \$9.99, with the winner earning the least possible amount of money – 1 cent – from the \$10 won. In a Tullock auction, however, every bidder has to pay their price. A bidder may decide that instead of paying \$9.99 and risk losing that amount, he will bid \$10 in order to win the \$10 back and have a zero net transaction instead of a loss of \$9.99. The next logical person may bid \$10.01 to win and incur a loss of just 1 cent. The next person could bid \$10.05, and so on. Now people are bidding not to maximize their profit but to minimize their losses. If they bid below their value there will be someone who can bid above. If they bid at their value they risk not winning the bid and losing their value anyway. Therefore they will bid above their value in order to minimize the amount they will lose.

This may seem like a rather silly kind of auction – who would voluntarily participate in a Tullock auction and pay above their value? However, as Munger explains, any promise to give away money for free – in other words, a grant – creates the setting for a Tullock auction. He gives the example of the United States Housing and Urban Development (HUD) grants. Cities vie for these grants to get money to improve public parks, develop housing projects for the poor, maintain rail systems, etc. HUD reviews the grant applications very carefully to ensure that only the city with the best application gets the money. Ideally, no city will spend money trying to get the grant, so the entire value of the grant is obtained for ‘free’. Now, if a well-meaning councilman (no oxymoron intended!)  wants his city to win a \$5 million grant, he might not mind paying \$1 million to hire people to write the grant application well. This money will come out of taxes and public funds, but if it helps the city win the grant, there is \$4 million to be gained. What if there are 10 cities that think this way? All 10 cities will take \$1million out of public funds – \$10 million. Only 1 city wins the \$5 million grant. Net result: \$5 million of tax-payers money is lost. In fact, according to the podcast, nearly a quarter of the grant money that cities win is spent trying to obtain the grant in the first place. Presumably the same amount is spent by cities that don’t win the grant. These cities would like to get the grants for free, but the competition inherent in the HUD evaluation means that they have to engage in a Tullock auction and risk running losses in order to win.

Tullock auctions are not limited to HUD grants; even NIH grants create a Tullock auction where the unit of transaction is time instead of money. Ideally, if a researcher’s work is good enough, they should be handed the grant at no cost. However, researchers trade their valuable research time for time spent writing the grant application. These people are encouraged not to ‘bid’ if they see no reasonable chance of winning, i.e. they are encouraged to evaluate whether applying for the grant is worth their time or if the time taken away from research for administrative tasks will outweigh the value of the grant itself. Even so, multitudes still apply for the grant and many of those people find themselves bidding at a loss. If we take the phrase “time is money” literally, it is disheartening to think that the aggregate of the time wasted is more valuable than the grant itself. Even for the winner, the money isn’t ‘free’ – it is used in part to compensate the wasted time used in the application process (and still may not be enough!). It is clear that ‘free money’ is not actually free – the competition that ‘free money’ invokes results in a loss of resources among the bidders as they bid above their value.

From this discussion we see that in Tullock auctions, logical bidders will bid above their value, be it in terms of time or money. This means that they bid at a loss, and their goal is to minimize their losses. However, this is not an ideal situation particularly in the public sector. When the goal is to help the public, be it through helping needy cities or facilitating better research, having city planners and researchers squander time or money in competing in these auctions actually results in losses for the public. To an individual bidder who loses the auction, the loss may be hard to bear. To the public which bears the brunt of the sum of losses, it is even harder. If this auction format for handing out ‘free money’ could be substituted with a different system of incentives for those who compete for grants, it might help the public recover its losses from the Tullock system. The most logical course of action is to not lose at all.

Main source:

Giving Away Money: An Economist’s Guide to Political Life (http://www.econtalk.org/archives/2006/06/giving_away_mon.html)

Other sources:

http://www.scientificamerican.com/article.cfm?id=dr-no-money

http://thisiscommonsense.com/tag/tullock-auction/