Internet Advertising and Optimal Auction Design Michael Schwarz

1. Internet Advertising and Optimal Auction Design Michael Schwarz Yahoo! ResearchNIPS Workshop: Beyond Search: Computational Intelligence for the Web December 2008

2. Four for One Special • Optimal Auction Design in a Multi-unit Environment: The Case of Sponsored Search Auctions (with Edelman) • Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords, (with Edelman, Ostrovsky) AER, March, 2007 • Greedy Bidding Strategies for Keyword Auctions (with Cary et al.), EC 2007 • Ad Auction Design and User Experience, (with Abrams), Special Issue of Applied Economics Research Bulletin on Theoretical, Empirical, and Experimental Research on Auctions, 2007 Main topic of this talk

3. Humorous History of Market Design Wife auctions, Babylon, 5th century BC Market design, matching theory, second half 20th century, US Moving from a metaphor to reality, Everywhere, now • Note: Vickrey (1961) did not invent Vickrey (second price) auction • Gale, Shapley (1962) did not invent deferred acceptance algorithm • Over time mechanism design moved from being primarily a metaphor describing markets to a tool that shapes them • Everything in the economy is a mechanism e.g.: • A worker negotiating with employers can be modeled as an auction • Matting can be modeled as a deferred acceptance algorithm

4. Mechanism Design– Literal Interpretation • Literal interpretation of words “mechanism design” are increasingly appropriate • FCC conducting a spectrum auctions • Medical residency match is a reality • This in turn gave rise to a number of interesting algorithmic and data mining problems that are of both theoretical and practical importance.

5. “Designed Mechanisms” v. “Metaphors” in the Internet Age • Until recently there was a sharp distinction between situation were mechanism is a "metaphor (or a model)" vs. "designed mechanisms". In the former case the underlying rules of the game are complex and implicit---the economic reality only roughly resembles the simple rules of mechanism design models. In the later case the rules tend to be fairly simple and explicit. • Recently, a new trend emerged---mechanisms that are designed (in a sense that the rules of the game are explicitly specified in a market run by a computer program), yet the rules of the market place are complex and as long as market participants are concerned the rules are implicit because they are not fully observable by market participants. • The market for sponsored search is perhaps the first example of such marketplace-- the mechanism used for selling sponsored search advertisement is better described by words "pricing mechanism" than an auction. In essence, when machine learning meets mechanism design we end up with a "designed mechanism" that shares some features of unstructured environment of the off line world. As mechanism becomes enriched with tweaks based on complex statistical models the rules become complex enough to be impossible to communicate to market participants.

8. History • Generalized First-Price Auctions 1997 auction revolution by Overture (then GoTo) • Pay per-click for a particular keyword • Links arranged in descending order of bids • Pay your bid Problem. Generalized First-Price Auction is unstable, because it generally does not have a pure strategy equilibrium, and bids can be adjusted dynamically

11. History (continued) • Google’s (2002) generalized second-price auction (GSP) • Pay the bid of the next highest bidder • Later adopted by Yahoo!/Overture and others

12. GSP and the Generalized English Auction • N≥2 slots and K = N +1 advertisers • αi is the expected number of clicks in position i • sk is the value per click to bidder k • A clock shows the current price; continuously increases over time • A bid is the price at the time of dropping out • Payments are computed according to GSP rules • Bidders’ values are private information

13. Strategy can be represented by pi(k,h,si) si is the value per click of bidder i, pi is the price at which he drops out k is the number of bidders remaining (including bidder i), and h=(bk+1,…,bk) is the history of prices at which bidders K, K-1, …, k+1 have dropped out If bidder i drops out next he pays bk+1 (unless the history is empty, then set bk+1≡0).

14. Theorem. In the unique perfect Bayesian equilibrium of the generalized English auction with strategies continuous in si, an advertiser with value si drops out at price pi(k,h, si)= si -(si-bk+1) αk /αk-1 In this equilibrium, each advertiser's resulting position and payoff are the same as in the dominant-strategy equilibrium of the game induced by VCG. This equilibrium is ex post: the strategy of each bidder is a best response to other bidders' strategies regardless of their realized values. The above is from Edelman, Ostrovsky and Schwarz Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords, AER, March, 2007 Cary et al. EC 2007, shows that myopic best bidding strategies converge to the same equilibrium.

15. The Intuition of the Proof First, with k players remaining and the next highest bid equal to bk+1, it is a dominated strategy for a player with value s to drop out before price p reaches the level at which he is indifferent between getting position k and paying bk+1 per click and getting position k-1 and paying p per click. Next, if for some set of types it is not optimal to drop out at this "borderline" price level, we can consider the lowest such type, and then once the clock reaches this price level, a player of this type will know that he has the lowest per-click value of the remaining players. But then he will also know that the other remaining players will only drop out at price levels at which he will find it unprofitable to compete with them for the higher positions.

16. Optimal Mechanism Assume that bidder values are iid draws from a distribution that satisfies the following regularity condition: (1-F(v))/f(v) is a decreasing function of v. Proposition. Generalized English auction with a reserve price v* is an optimal mechanism, where v* denote the solution of (1-F(v))/f(v) =v Note: The optimal mechanism design in multi-unit auctions remains an open problem. Note: Reserve price does not depend on the rate of decline in CTR, on the number of positions and on number of bidders From Edelman and Schwarz Optimal Auction Design in a Multi-unit Environment: The Case of Sponsored Search Auctions

17. Percent increase in search engine revenue when search engines set optimal reserve prices

18. Total increase in each advertiser's payment, when reserve price is set optimally versus at $0.10

19. Theorem. Reserve price causes an equal increase in total payments of all advertiser whose value are above reserve price.

20. Yahoo! Research is not Just About Sponsored Search • Median Stable Matching (with Yenmez) • Standard two sided matching market with wages (in discrete increments) • There exists finite set of stable matches (buyer and seller optimal matches are extreme points of this set) • We show that median stable match exists i.e. a match that is median for every agent at the same time