Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords BENJAMIN EDELMAN, MICHAEL OSTROVSKY, AND MICHAEL SCHWARZ American Economic Review, vol. 97(1), March, 2007 Bo Zhou

Generalized First-Price Auction Advertisers get positions according to their bids. Each one pays exactly the amount of his or her bid for each click. Suppose we have three bidders and two advertising positions with CTRs of 200 and 100, respectively. Advertiser Per-click Value Bid Payoff Windows 10 4.01 1198 Mac 4 2.01 199 Linux 2

Generalized First-Price Auction But smart advertisers always try to minimize costs. Advertiser Per-click Value Bid Payoff Windows 10 2.02 1596 Mac 4 2.01 199 Linux 2 Advertiser Per-click Value Bid Payoff Mac 10 2.03 394 Windows 4 2.02 798 Linux 2

Generalized First-Price Auction Using GFP, the auction can be extremely volatile, even chaotic. Bidders have strong incentives to “game” the system by slightly outbidding the advertiser right above. The ad sellers ultimately swallow the loss. Consider the following example in which Windows employs a bidding robot while both Mac and Linux bid manually. Advertiser Per-click Value Bid Payoff Windows 10 2.02 1596 Mac 4 2.01 199 Linux 2

Vickrey–Clarke–Groves Auction (VCG) Advertisers get positions according to their bids. Each one pays the “externality” he or she imposes on others by taking one slot away. A B C D A C D B should pay what C and D lose. Advertiser Per-click Value Bid Payment Payoff Windows 10 600 1400 Mac 4 200 Linux 2

VCG Auction Truth-telling is a dominant strategy under VCG. A dominant strategy performs at least as well as any other strategy in any situation. Simply put, it is one of your best responses to the auction. Still, ad seller’s revenue suffers.

Generalized Second-Price Auction Advertisers get positions according to their bids. Each one pays the amount of bid of the advertiser right blew for every click. Consider the following example where everybody bids truthfully. Advertiser Per-click Value Bid Payment Payoff Windows 10 4 1200 Mac 2 200 Linux It appears that nobody has any incentive to shift bidding strategy because nobody will be better off by doing so!

Generalized Second-Price Auction This situation is called an equilibrium. In an equilibrium, everyone chooses the best strategy by taking into account every other’s strategy. In other words, nobody can be better off by shifting strategy unilaterally. The example on the last slide shows that using truth-telling strategy under GSP can produce equilibrium. From an bidder’s perspective, using truth-telling strategy under GSP can maximize its payoff. Just sometimes!!!

Generalized Second-Price Auction Let’s consider a similar example where the CTRs of both positions are now 200 and 199. If all three bidders stick to the truth-telling strategy. Advertiser Per-click Value Bid Payment Payoff Windows 10 4 1200 Mac 2 200 Linux However, what if Windows decides to change course? Advertiser Per-click Value Bid Payment Payoff Mac 4 3 200 Windows 10 2 1600 Linux

Locally envy-free Equilibrium Equilibrium looks fine, but is it stable? Not necessarily. An advertiser may have incentives to behave aggressively to swap positions with the advertiser right above him or her.

Locally envy-free Equilibrium Now CTRs change to 300 and 100, respectively. Advertiser Per-click Value Bid Payment Payoff Windows 5 4 300 Mac 6 3 Linux Mac wants to provoke. Advertiser Per-click Value Bid Payment Payoff Windows 5 4.99 3 Mac 6 300 Linux

Locally envy-free Equilibrium Apparently, Windows would like to retaliate. Advertiser Per-click Value Bid Payment Payoff Mac 6 4.99 4.98 306 Windows 5 3 198 Linux Locally envy-free equilibrium is an equilibrium where no advertiser has any incentive to swap positions with the advertiser right above him or her. Locally envy-free equilibrium is stable.

Locally envy-free Equilibrium Construct a particular locally envy-free equilibrium where all advertisers’ payments coincide with their payments in truth-telling equilibrium in VCG. Advertisers are labeled in decreasing order of their values, i.e., if 𝑗<𝑘, then 𝑠 𝑗 ≥ 𝑠 𝑘 . 𝑏 𝑘 = 𝑝 𝑉, 𝑘−1 / 𝛼 𝑘−1 , 𝑏 1 = 𝑠 1 𝑏 𝑘 is advertiser k’s bid; 𝑝 𝑉, 𝑘−1 is the payment of advertiser k-1 in the truth-telling strategy equilibrium of VCG; 𝛼 𝑘−1 is position k-1’s CTR. Advertiser Per-click Value Bid Payment Payoff Windows 10 3 1400 Mac 4 2 200 Linux

A little history Generalized First-Price Auction GoTo (now called Overture under Yahoo!) invented GFP auction in 1997. It probably marked the start of pay-per-click era of Internet advertising. VCG Auction It was first proposed by Vickery in 1961. I have not found any evidence suggesting it was used by any major search engine. Generalized Second-Price Auction GSP was first introduced by Google in 2002. Yahoo! switched to GSP soon after.

Why GSP, not VCG? VCG seems to be such an elegant mechanism. In fact, William Vickery won a Nobel Prize for it. GSP appeared first. So, it has the upper hand. VCG is hard to explain. Switching is expensive. Revenue prospects are uncertain.