1. 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

2. 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

3. 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

4. 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

5. 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

6. 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.

7. 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!

8. 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!!!

9. 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

10. 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.

11. 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

12. 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.

13. 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

14. A little history Generalized First-Price Auction
GoTo (now called Overture under Yahoo!) invented GFP auction in 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 Yahoo! switched to GSP soon after.

15. 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.