An Overview of some Basic Properties of Sponsored Search Auctions

There are m positions to be allocated among n bidders, where n > m. We assume that the (expected) click-through rate of bidder i in position j is of the form αiγj , i.e. separable into an advertiser effect αi ∈ [0, 1] and position effect γj ∈ [0, 1]. We assume that γ1 > γ2 > . . . > γk > 0 and let γj = 0 for j > k. We will sometimes refer to αi as the relevance of bidder i. It is useful to interpret γj as the probability that an ad in position j will be noticed, and αi as the probability that it will be clicked on if noticed. Bidder i has value vi for each click. Bidders have quasi-linear utility, so that the utility to bidder i of obtaining position j at a price of p per click is