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Telling the Truth
The other day I drove by a church on Pleasant Home road. "Spaghetti dinner and auction," it said on a sign next to the church. We economists have done our bit of thinking about auctions. The problem is the following: how does an auctioneer get bidders to truthfully reveal the amount at which bidders value the item on the block? Suppose an item is worth $250 to you. In the standard, ascending auction your incentive is never to reveal the full amount at which you value the item. Instead your incentive is merely to top the next bidder. Say the auction begins at $50. The bidding seesaws back and forth. If the auction price reaches beyond $250, your silence reveals your true valuation and you are out of the running. But if the auction stops at $175 you saved, by not telling the truth, $75. You also made the church $75 poorer than it could have been. Shame on you? Or shame on the auctioneer for using a poorly-designed auction mechanism? What other auction designs are available? One is the sealed-bid auction, where each contestant leaves an envelope with a single bid. The highest bid is accepted (or, in the case of service contracts, the lowest bid). But even here there exists an incentive not to tell the truth. The reason is that, strategically, it is in your interest to bid just above what you believe the next contestant's envelope contains. In other words, you are bidding not on the item, but against your competitor. In the church example, if you believe that the next highest bid will be $174, then you will bid $175 to win – and save yourself, again, $75 relative to your true valuation of $250. What about the reverse auction? Here the auctioneer starts with a top price, say $400 and gradually lowers it until someone bites: $390, $380, $370, $360, $350, $340, $330 ... The tension in the audience rises – until you can't stand the pressure anymore and snap at $320 because you fear that someone else might get the item first. In this case, you paid $70 more than you value the item at – and the church turns an unfair dollar. This is an example of the "winner's curse," where winners are induced to overpay their true valuation of the items. Shame on the church for putting the curse on you? So, what's the problem? The problem is that all these auctions link your bid to someone else's bid, instead of linking your bid to the auction item itself. To get you to reveal the truth we must cut the link between you and the other bidders. Instead, we must link your bid to the value of the item. In 1961, Prof. William Vickrey of Columbia University in New York City, and co-recipient of the 1996 economics Nobel-Prize, came up with a clever strategy to get you to tell the truth. His second-price auction works as follows: the highest bidder wins but pays the second-highest bidders price. So, suppose the item on the church auction block is worth $250 to you and $230 to another fellow in the audience. You submit a secret bid of $250, the other fellow submits a secret bid of $230. When all bids are revealed (opened), you win the item but pay only $230. Why does this work? Suppose that you continue to hide the truth and submit a bid of only $175. It that case, the other person would have won, bidding $230 but paying $175. We learn three lessons. First, dishonesty does not pay (you don't get the item). Second, it does pay to act truthfully (you do get the item). Third, to force truth-revelation is costly – after all, the church still gets only $230, even though you valued the item at $250. If nothing else, we are now on the path of righteousness. You see, truth-telling – even in church – requires some clever thinking. Now enjoy your spaghetti dinner.
Dr. J. Brauer is Professor of Economics at Augusta State University's College of Business Administration. He can best be reached via his web site (http://www.aug.edu/~sbajmb). |