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How Market Designs Set Prices

Hal Varian (Chief Economist, Google) recently shared a concise article with the title “How auctions set ad prices”. The article is a clear exposition of how ad prices determine the sorting order of bidders for online advertising. However, the tone of the article is not quite compatible with how it feels from the outside.

Roughly the first idea for ad bidding is to use a traditional auction and to sort bidders by price. That is the highest bidder is given position one and the next highest bidder is given position two and so on. There is some sophistication in that each bidder can be asked to pay (if their ad is clicked) a minimum increment more than the bid of the maximum-bid of the position below them. This variation (often called “Vickrey”) makes the auction a little more dynamic in that it simulates each bidder lowering their bids to the minimum amount that would have yielded them the position they have been awarded.

The second idea is to not sort by bids, but instead sort by bid times an estimate of click-through probability. This was a simple and brilliant idea. With this innovation bids are now sorted in terms of their “expected value.” This is because in “pay per click” advertising the ad-bidder pays only if their advertisement is clicked on. When we say the bids are now sorted in terms of “expected value” we mean that the bids are now sorted in terms of how much money the advertising supplier can expect to make. A low-quality ad that has no chance to be clicked on (and thus will generate no revenue) is no longer sorted behind slightly lesser bids from more lucrative bidders.

The third idea is where the explanation becomes difficult to follow. A second adjustment factor called “Quality Score” (meant to reflect the quality of the web site and page the advertisement is pointing to) is introduced. How is this quality score determined? Here is a quote from the original article:

“Where does this Ad Quality Score come from? It was originally determined by historical click through rates but has been refined over the years using sophisticated statistical models.”

The phrase “sophisticated models” signals that the quality score can not be reproduced and estimated by bidders (unlike click-through probability). So bidders do not really know what the quality score is. I admit I do not know what the quality score is, but I do know something one could (in theory) do with it.

Suppose for a single ad-word you had two bidders named Cain and Abel that both are willing to bid $1.00 for their ad to be in the first position (a common situation). Further suppose that each bidder is willing to spend a fixed amount per-day and stops bidding when their daily budget is exhausted (a common bidding policy). If Abel has a much smaller budget than Cain then Abel may run out of money early in the day and be removed from later auctions in the day. From that point on Cain can place ads in position one for the minimum bid (maybe $0.10) and a lot less money changes hands (than when Abel was in the auction). If, however, Abel was given a special quality score that just happened to be such that the ratio of Abel’s quality score to Cain’s quality score was around the same size as the ratio of Cain’s daily budget to Abel’s daily budget then things change radically. With this higher quality score (remember Cain’s budget is larger so by our description Abel’s quality score is larger) Abel can compete with Cain’s ad with a deeply discounted bid. This additional bidding power is exactly what is needed to keep Abel in the auction for the whole day. This in turn is exactly what is needed to make Cain bid higher competitive prices (instead of minimum bid) for the whole day. The additional money extracted from Cain can far exceed the discount given to Abel.

At this point many bidders might wish for a more transparent “Quality Score.”

A great technical article describing this kind of mathematics is: “AdWords and Generalized On-line Matching” Aranyak Mehta, Amin Saberi, Umesh V Vazirani and Vjay V Vazirani (2006).

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