Auction Theory by Vijay Krishna
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Research by Ostrovsky, assistant professor of economics; Benjamin Edelman, doctoral candidate in economics at Harvard University; and Michael Schwarz, RWFJ Scholar at the University of California, Berkeley, and Faculty Research Fellow at the National Bureau of Economic Research, shows how the current mechanism could be adjusted to create an auction that better serves advertisers—although such an adjustment may not necessarily financially benefit search engines. “At the very least, we want to educate advertisers about the fact that in some sense they are being taken advantage of. Under the current mechanism, if they don’t think carefully about their bidding strategies, they can end up paying a lot more to the search engines than they need to,” Ostrovsky says.
At issue, he explains, is the fact that the search engines Google and Yahoo are not using the original version of the auction for which William Vickrey won the Nobel Memorial Prize in 1996. The auction Vickrey designed has a remarkable property: The best strategy for the buyers is to bid precisely what they feel the item in question is worth to them. “Google says that its mechanism uses the ideas of the Vickrey auction, but fails to mention some important differences, which creates confusion,” says Ostrovsky. “Such a claim gives advertisers the misconception that they should bid as much as they’re willing to pay.”
Google and Yahoo earn revenues by charging advertisers who participate in auctions each time a user clicks on that advertiser’s site. What advertisers purchase is the right to have a link to their website appear in strategic positions on pages that pop up when users conduct keyword searches for terms associated with that buyer’s business (such as “car insurance,” “travel,” and so forth). What they bid is a specified amount per click—anywhere from a few cents to as much as $10, or even more.
Rather than paying the amount they’ve bid, however, in the current auction system advertisers are charged only a penny more per click than the next lowest bid, with some adjustments that depend on the quality of the ad. The search engines have billed this setup as one that should encourage auction participants to bid truthfully, since they ultimately pay less than what the click is worth to them. Ostrovsky says discerning bidders, however, see that underbidding is often still the wiser strategy. “It’s not a true Vickrey mechanism,” he says. This setup may result in volatility, he notes, with bids fluctuating from moment to moment as advertisers scramble to respond to one another. Such instability means that ad placements are often in flux as the search engine computers continually recalculate rankings.
In a true Vickrey auction, an advertiser would indeed be charged less than his actual bid, but the precise figure would be calculated differently. It would amount to the measure of the “externality”—or the value of lost clicks—he imposes on others by pushing them down in the ranking from, say, the number two to the number three slot. “For example,” says Ostrovsky, “suppose there were three advertisers truthfully bidding 10, 8, and 7 dollars per click, respectively, and three advertising slots, receiving 100, 70, and 50 clicks per hour. Then the presence of the first advertiser moves the second one from the top position to the next one, thus costing him 30 clicks per hour at $8 per click, and moves the third advertiser from the second position to the third one, costing him 20 clicks per hour at $7 per click. Hence, the total externality that the first advertiser imposes on others is $240 plus $140 equals $380 per hour, and he would be charged $3.80 per click in a Vickrey auction. Remarkably, under this pricing scheme, it is optimal for each advertiser to bid his actual value per click, regardless of what other advertisers do.”
In contrast, under the current auction system that is often not the case. In the above example, the first advertiser would be charged $8.01 per click, giving him 100 clicks per hour and leaving him with the profits of approximately $200. If, however, he reduced his bid from $10 to any value less than $7, he would be placed in the third position. He would receive only 50 clicks per hour, but would pay only a very minimal price, giving him much higher profits.
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