Optimization Problems in Internet Advertising

1. Optimization Problems in Internet Advertising Cliff Stein Columbia University Google Research

2. Internet Advertising • Multi-billion dollar business • Google purchased DoubleClick for over 3 billion dollars, 2 years ago • A new paradigm for advertising • Many interesting mathematical, economic, and computational problems

3. Some Statistics VendorAd viewers Google 1,118 DoubleClick 1,079 Yahoo 362 MSN 309 AOL 156 Adbrite 73 Total 3,087 (millions, one month in 2008) **From Wikipedia

4. Internet Advertising • 2 main types • Adwords (right column, auction) • Display ads (scattered, matching)

5. This talk • Overview of some issues in internet advertising • Talk about two particular algorithmic results, one on adwords optimization, one on display ads • No attempt to comprehensively survey the area

6. Adwords • Advertisers bid to have the right to appear when a user enters a search query • Advertisers are chosen according to some kind of auction mechanism • Ads are displayed for free. Advertiser pays when a user clicks.

15. New Kind of Auctions • Traditional auctions are for one item, or a small number of items, and are done on a human time scale • Many types of auctions (ascending, sealed-bid, second price …) are well understood mathematically • Adwords auctions are a new type of auction, where a bidder bids on multiple items for many items on a “computer” time scale • Mathematically, it is a whole new ballgame

16. Technical Challenges • Mechanism Design - designing rules of a game or system to achieve a specific outcome, even though each agent may be self-interested • Technology to implement the auctions • Optimization for • Advertiser (maximize clicks, minimize money spent) • Internet company (maximize profit, maximize user happiness, minimize bad publicity/lawsuits)

17. Basic Mechanism Design • Let’s set up an auction for • Suppose it is worth $20 to me, but $10 to Alex Rodriguez (and these values are private) • We each bid some amount: • Who gets the hat? • How much do they pay?

18. Basic Mechanism Design Bidders Private value 1 Bid 1 Auction Mechanism Gives item to someone Collects payments Private value 2 Bid 2

19. Some goals in an auction • Truth revealing (bidders want to bid their values) • Revenue maximizing (auctioneer maximizes profit) • Social welfare (good for bidders) These goals may be in conflict

20. First price auctions • Everyone bids, highest bidder gets item for the price he bid, others pay nothing and get nothing. • Bidders Utility = value of item received – payment.

21. First price auction Me $20 Bid 20 First Price Auction Mechanism Cliff gets it. Cliff pays $20 Arod pays $0 Arod $10 • My utility = $20 - $20 = 0 • Arod utility = $0 - $0 = 0. Bid 10

22. Can I do better?

23. First price auction (2) Me $20 Bid 15 First Price Auction Mechanism Cliff gets it. Cliff pays $15 Arod pays $0 Arod $10 • My utility = $20 - $15 = 5 • Arod utility = $0 - $0 = 0. Bid 10

24. First Price Auctions Suppose I bid $15, Arod bids $10. • I get item for $15, Arod gets nothing for nothing. • My utility = 20- 15 = 5 • Arod utility = 0-0 = 0 • I am happier • I am not telling the “truth” anymore • My bid needs to be a function of everyone else’s bid (in addition to my value) • Auctioneer makes less money

25. Second Price Auctions • Everyone bids. Item goes to the highest bidder, who pays the bid of the second-highest bidder. • Bidders Utility = value of item received – payment

26. Second price auction Me $20 Bid 20 Second Price Auction Mechanism Cliff gets it. Cliff pays $10 Arod pays $0 Arod $10 • My utility = $20 - $10 = 10 • Arod utility = $0 - $0 = 0. Bid 10

27. Second Price Auctions Theorem: In a second-price auction, no bidder has any incentive to lie. Proof: I don’t lie. • If I lie any amount >= 10, nothing changes. • If I lie < 10, I lose the auction and my utility is 0. • Therefore I don’t want to lie.

28. Second Price Auctions Theorem: In a second-price auction, noone has any incentive to lie. Proof: Arod doesn’t lie. • If he lies any amount < 20, nothing changes for him. • If he lies at x > 20, he wins for $20, but his utility is 20 –x which is negative, so he is worse off.

29. Notes on Second Price Auctions • Everyone tells the truth • May yield less revenue than first-price auctions • Note: we assume that I get no benefit from seeing you pay more money.

30. Back to internet auctions • We are not auctioning off baseball hats, or paintings, or cars that were used in the commission of a crime…. • We are auctioning off slots on a web page • There are: • Multiple slots • Advertisers bidding on many keywords • Many auctions going on during the course of a day

31. Multiple Slots: Generalized Second Price Auctions • Users are bidding for slots, where slot i is more valuable than slot i+1. • Higher slots tend to get more clicks, and therefore cost more (cost per click) • Sort bids, i’th bid gets slot i and pays bid of slot i+1.

32. Example of GSP Auction • Bids: $1, $0.50, $2.25, $1.20, $0.10, $2.50, $1.25 • 5 slots

33. Example 2 of GSP Auction • Bids: $1, $0.50, $2.25, $1.20, $0.10, $2.50, $1.25 • 5 slots

34. Some Complications from GSP • We are bidding one amount, but don’t know which slot we will win. • Different advertisers have different preferences/beliefs about slots • You actually might have some incentives to lie. In “reality” (google), your bid is actually modified by the “quality” of your ad.

35. Advertisers bidding on many keywords • An advertiser sets up a campaign in which they advertise on many keywords • Each time a user issues a query that matches one of their keywords, the ad for that keyword enters the auction. • Depending on their bid (and other factors), they may get a slot in the auction • If someone clicks on their ad, they are charged

36. Question? • How does the advertiser control the total amount that they are charged? They specify a budget on how much they want to spend in a day

37. Budgets • Advertiser specifies a daily budget B. • They participate in an auction as long as the daily budget is not spent.

38. Example

39. Example • Auction 1: Hiking. Joe wins. When click happens, he pays $0.75

40. Example • Auction 1: Hiking. Joe wins. When click happens, he pays $0.75

41. Example • Auction 2: Skiing. Campmor. When click happens, he pays $0.50

42. Example • Auction 2: Skiing. Campmor. When click happens, he pays $0.50

43. Example • Auction 3: Hiking. Joe wins. When click happens, he pays $0.75

44. Example • Auction 3: Hiking. Joe wins. When click happens, he pays $0.75

45. Example • Auction 4: Hiking. Joe should win. But he doesn’t have enough budget, so Campmor wins. Pays some amount < 0.75 (depends on other bidders and system minimums).

46. Lessons • Auction is not always won by the highest bidder. • Bidders may engage in strategic behavior, allow others to win at a high price so as to exhaust their budget and be removed from competition (bid jamming)

47. What about the advertiser? • Suppose you are an advertiser • You want to bid on many keywords • How should you allocate your budget among multiple keywords?

48. Example: Asics • Keywords: Shoe, sneaker, running shoe, gel kayano, gel nimbus, pronating, marathon shoe, race shoe, reebok, I hate asics, sporting goods, footware, racing attire, race, wicked fast, air jordan, laces, shin splints, white sneakers, … • Budget: $100 • What to bid on each one?

49. Who advertises adwords?

50. Optimization Problem • Suppose that I knew • Everyone else’s bids • Exactly how many times each keyword will come up • The number of clicks associated with each position • Google’s exact advertising mechanism How should I bid? (Note: Think of bid as cost-per-click (cpc))