THE GOOGLE AD AUCTION

The Google ad auction is probably the largest auction in the world, with billions of auc­tions being run per week. It turns out also to have a very nice theoretical structure as described in Edelman et al.

To see how this works, consider a bidder who is contemplating entering a keyword auction. The current participants are each bidding some amounts. Hence the new bidder thus faces a ‘supply curve of clicks’. As it bids higher it will displace more of the incum­bent bidders, leading to a higher position and more clicks. In choosing its bid, the adver­tiser should consider the incremental cost per click: how much more money it will have to spend to get additional clicks. If the incremental cost per click is less than the value per click, the advertiser should increase its bid; if the incremental cost per click is less than the value per click, it should decrease its bid. In equilibrium the incremental cost of moving up one position should exceed the bidder’s value per click, but the incremental savings from moving down one position should be less than the bidder’s value per click.

This has the implication that in equilibrium the incremental cost per click should be increasing in the click-through rate. Why? Suppose it decreased in moving from one position to the next. Then there was some bidder who purchased expensive clicks but passed up cheap ones, contradicting the assumption of equilibrium. Furthermore, since the value per click should be bounded by the incremental cost per click in equilibrium, the observed incremental costs allow us to infer valuable information about the bidders’ values. In practice, incremental cost per click seems to give a plausible estimate of click value. However, it is important to note that there is still a certain indeterminacy of equi­librium. The requirement that each agent prefers its position to other possible positions does not pin down a unique outcome. Rather it determines a range of equilibrium bids. Two particularly interesting equilibria are the ones that yield the maximum and the minimum revenue for the search engine.

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