# Nasty Auctions

Imagine a professor who holds up a \$20 bill in a class and auctions if off to the high bidder. What do we expect to happen? It would make no sense for anyone to anyone to bid higher than \$20, and if the high bid is below \$20, someone in the class will have an incentive to bid a bit higher. The end result is that the \$20 bill should fetch a high bid of something very close to \$20, if not \$20 itself. This image of people bidding up the value of an item to its true value is used repeatedly when economists discuss markets. However, auctions are not always so nice.

Imagine instead that the professor presents his class with a bottle of coins. He lets them inspect the bottle, but they cannot open it and it is impossible to count the money in the bottle. He then asks everyone to write down a bid, and accepts the high bid. When this experiment is run in actual classrooms, the end result is that the average bid is less than the value of the bottle, because people are risk-adverse and will bid less than they what the expect the value to be. Some people err in underestimating the value of the coins in the bottle, but others err in overestimating their value. Usually one of the people who overestimate the value ends up winning the bid, and it is very common for the bid to be higher than the true value. Economists have dubbed this phenomenon "the winner's curse," and find it a feature of bidding for oil-exploration rights and for free-agent baseball players.

Finally, there is another sort of auction--called the entrapment game--that is particularly nasty. Suppose that anyone who bids at the auction of our \$20 bill must pay the amount of the bid whether he wins or not. Someone will open the bidding low at \$.50 in hopes of getting a real bargain. Someone else will top the bid with a \$1 bid. Bidding will usually proceed up to about \$10 and then pause. The second bidder must now decide whether to lose his \$8 or \$9 bid, or continue. If he continues, the bidding will usually advance up to \$20 and then pause again. The second highest bidder now realizes that he is not going to gain anything on this auction, but has the potential for a substantial loss, so he has a strong temptation to up his bid beyond \$20. Here is how Frank and Cook describe this game:

"One might be tempted to think that any intelligent, well-informed person would know better than to become involved in an auction whose incentives so strongly favor costly escalation. But many of the subjects in these auctions have been experienced business professionals; many others have had formal training in the theory of games and strategic interaction. For example, psychologist Max Bazerman reports that during the past ten years he has earned more than \$17,000 by auctioning \$20 bills to his MBA students at Northwestern University.... In the course of almost two hundred of his actions, the top two bids never totaled less than \$39, and in one instance totaled \$407."1

Though you may be tempted to think that such auctions never happen, they may in fact describe a common phenomenon in situations where there is only one winner, which happens frequently in rent-seeking situations. For example, consider the competition for an Olympic gold medal in figure skating. The winner (and perhaps the runner-up) will earn considerable money in endorsements, whereas the rewards to those finishing out of the medals will be much less. One bids for this medal by investing time and money for practice, and that time is lost both for winners and losers. It can easily happen that the total value of the money and time for all those who compete, including all those who never make it onto an Olympic team, far exceed the value of winning.

1 Robert H. Frank and Philip J. Cook. The Winner-Take-All Society, New York: The Free Press, 1995., pp. 129-30.