PLATFORMS: REVIEWS, RATINGS, AND RECOMMENDATIONS 1
III. BRIEF HISTORY AND ECONOMIC ANALYSIS OF THE SPONSORED SEARCH AUCTIONS
1. Pre-history: Overture and the GFP Auction
In 1998, the search engine GoTo.com revolutionized the world of online advertising by introducing auctions to sell ad space on its search results pages. This company, later renamed Overture and acquired by Yahoo! in 2001, had devised the so called Generalized First Price (GFP) auction, in which advertisement space was assigned to advertisers by the ranking of their bids, with each advertiser paying his own bid for each click he received. The key idea was to realize that a search engine was able to harvest a very valuable good:
consumers’ attention. The next step was then to turn every search on the search engine into an auction. The scheme first developed by GoTo.com-Yahoo!, and subsequently followed by all other search engines, was essentially to generate a distinct auction for every keyword searched on the search engine.
In Yahoo!’s original format, the GFP auction, slots were assigned to bidders in decreasing order of bids (the best slot to the highest-bidder, the second slot to the second-highest bidder, and so on), and every bidder paid a price-per-click equal to his own bid. Hence, suppose that the n bidders submit a profile of bids b = (b1, b2, ..., bn), and i’s bid is the k-highest, then he obtains slot k and pays a price-per-click equal to his own bid. The resulting payoff for this bidder is therefore xk. (vi − bi). Each advertiser is thus restricted to one bid per keyword, without the possibility of indicating a different price for different slots.11
This auction format was initially very successful. Yahoo!’s revenues and capitalization grew very quickly. But as Yahoo!’s auctions grew in volume, and advertisers became acquainted with their operation, this initially very successful model became problematic (see, for instance, Ottaviani, 2003). The reason is that, after an initial period in which advertisers cycled through phases of aggressive and conservative bidding, their bids eventually settled at very low levels. This meant more volatile and overall lower revenues for Yahoo!, which was therefore vulnerable to competition from other search engines which could devise better auction formats. But to understand which features of an auction would make it overcome this kind of problems, it is important to first understand
11 An alternative that has been experimented by search engines, but without ultimately being adopted on a large scale, involved a form of “combinatorial bidding” allowing advertiser to bid either for a regular slot or for a larger slot containing not only a short text message, but also a larger picture.
why the GFP auction may have generated these phenomena of bidding cycles and implicit bid collusion. For this reason, we turn next to an economic analysis of the GFP auction.
1.1. Economic Analysis of the GFP Auction
Similar to the baseline (single-good) first-price auction, it can be shown that when advertisers are uncertain about others’ valuations, there exists an equilibrium of the GFP in which slots are assigned efficiently. Namely, bidding strategies such that the resulting equilibrium bids
b ˆ
= (bˆ1, bˆ2, ..., bˆn) have the property that bˆ1> bˆ2> ... > bˆn, so that the highest valuation bidder (bidder 1) obtains the best slot, the second-highest valuation bidder (bidder 2) obtains the second slot, etc. This way, for all bidders who do get a slot (namely, bidders i = 1, ..., S), they each pay their own bid ˆbi, and the resulting payoffs are xi.(vi−ˆ bi).
Now, suppose that –for a given keyword-auction– the set of bidders and their valuations are fairly constant over time. If this is the case, then bidders would come to expect each other’s equilibrium bids to be more or less equal to bˆ= (bˆ1, bˆ2, ..., bˆn). But now consider the problem of bidder S, the one obtaining the lowest slot on sale: his payoff when everybody bids in this way is xS . (vS− bˆn).
Since in the GFP auction the price-per-click is equal to a bidder’s own bid, this payoff is decreasing in S’s own bid. Hence, ideally this bidder would like to lower his bid as much as possible, but without losing his slot. This means that he clearly cannot just set his bid to zero, or he would lose his slot. But if the profile of bids bˆ= ( bˆ1, ,bˆ2 ..., bˆn) is fairly stable, then this bidder knows that he would still obtain the same slot as long as he places a bid higher than the next lower bid, bˆS+1. Thus, bidder S would have an incentive to lower his own bid as long as this happens without losing his position. If nobody changes their bid in the meantime, this ideally would be all the way down to bˆS+1+
ε
(where we takeε
> 0 to be the smallest bid increment, e.g., a euro cent).It should be clear that the logic of this argument in fact applies to every bidder i: each i would obtain the i-th slot as long as bi > bi+1. But apart from that, one’s payoff from obtaining the i-th slot is maximized if bi is set to the lowest possible value which ensures that i obtains his ‘right’ position. This means that, from an initial period of bids more or less stable at bˆ = ( bˆ1, bˆ2, ..., bˆn), the payment structure of the GFP gives bidders strict incentives to start lowering their bids.
But now suppose that bidder i’s bid has been lowered as much as possible, without conceding his slot (e.g., suppose that bi = bˆi+1+
ε
). At this point, bidder160
Part II: Pricing Mechanisms and Search
i+1 obtains the i+1-th slot at a price equal to ˆ
bi, paying essentially the same as what that bidder i is paying for the i-th slot, which has a higher CTR. Hence, bidder i+1 would have an incentive to increase his bid over bi (say, to bi +1 = bi +
ε
= bˆi+1 + 2ε
): this way, he would obtain the higher slot, and hence higher CTR, with almost no change in the price he pays. But then bidder i, who had originally lowered his bid in order to lower his payment for the i-th slot, is now out-bid by i+1, and drops one position down. At this point, bidder i has an incentive to increase his bid again so as to re-gain his original position. Thus, the initial phase in which bidders start lowering their bids so as to lower their payments, given the original allocation, is followed by a phase in which bids are subject to an upward pressure, in an attempt to maintain the original position.But since the higher valuation bidders have a higher willingness to pay for any given slot, this race to the top eventually re-establishes the original ranking, and hence it leads back to the efficient allocation: a low valuation bidder would stop competing for any given slot earlier than a high valuation bidder would, and different bidders would drop out of the race in increasing order of their valuation. But once the race-to-the-top is over, and the efficient ranking of bidders is re-established, then we are back to the original situation: holding positions constant, each bidder who obtains a slot has an incentive to decrease his own bid. And so it happens, until bids are so low that the race-to-the-top begins once again, and so on. Thus, because of the property of the GFP auction that bidders pay their own bid, no deterministic profile of bids bˆ= (bˆ1, bˆ2, ..., bˆn) can form an ‘equilibrium’ of this auction, when bidders’ valuations are stable.
In summary, when there is uncertainty over bidders’ valuations, then the GFP auction admits an equilibrium which induces efficient allocations, just as in the baseline first-price auction with a single good. This is because the uncertainty over others’ valuations translates into uncertainty over their bids, which in turn prevents bidders from lowering their bids without risking their slot. However, when there is no uncertainty over valuations, then the GFP has no ‘pure strategy’
equilibrium: the only equilibria must involve some randomization (if there is no uncertainty in valuations, then such randomization must be directly in the bids placed by the advertisers).12
The ultimate reason why the GFP ended up inducing bidding cycles was therefore that, for many keywords-auctions, the set of bidders and their valuations didn’t present sufficient uncertainty to prevent the advertisers from engaging in the mechanism described above. The incentives to lower their bids were too strong, which in turn triggered the following reaction of aggressive bidding, and hence the cycle.
12 See, for instance, Edelman and Schwarz (2007), which first provided this explanation for the shortcomings of the GFP auction.
But once bidders have gone over a few of these cycles, then they also understand that there isn’t much of a point in triggering the race-to-the-top. It soon becomes clear that any such price war is doomed to be won by the higher valuation advertisers, and hence re-establish the original allocation, just with higher prices for everyone. Hence, after a few of such bidding cycles, advertisers realize that raising each others’ bids in order to alter the final allocation is a desperate attempt. They would thus stop doing that, and accept instead the same allocation at the low bidding profile. This way, the bidding cycles generated by the lack of pure equilibria in the GFP auction favored an indirect form of collusion among the advertisers, which in turn eroded the revenues generated by the GFP auction.