Internet Economics כלכלת האינטרנט

1. Internet Economicsכלכלת האינטרנט Class 8 – Online Advertising (part 2)

2. Sponsored search auctions Real (“organic”) search result Ads: “sponsored search”

3. Sponsored search auctions Search keywords keywords keywords Ad slots

4. Bidding • A basic campaign for an advertiser includes:

5. Click Through Rates • Are all ads equal? • Position matters. • User mainly click on top ads. • Need to understand user behavior.

6. Click Through rate 0.5% 9% 4% 0.2% 2% 0.08%

7. Click Through rate c4 c1 c2 … c3 … ck

8. Formal model • n advertisers • For advertiser i: value per click vi • k ad slots (positions): 1,…,k • Click-through-rates: c1 > c2 > …> ck • Simplifying assumption: CTR identical for all users. • Advertiser i, wins slot t, pays p.utility: ct (vi –p) • Social welfare (assume advertisers 1,..,k win slots 1,…,k) :

9. Example The efficient outcome: v1=10 Slot 1 c1=0.08 Slot 2 v2=8 c2=0.03 Slot 3 c3=0.01 v3=2 Total efficiency:10*0.8 + 8*0.03 + 2*0.01

10. GSP • The Generalized Second price (GSP) auction • I like the name “next-price auction” better. • Used by major search engines • Google, Bing (Microsoft), Yahoo Auction rules • Bidders bid their value per click bi • The ith highest bidder wins the ith slot and pays the (i+1)th highest bid. • With one slot: reduces to 2nd-price auction.

11. Example b1=10 Slot 1 c1=0.08 Pays $8 Slot 2 b2=8 c2=0.03 Pays $2 Slot 3 c3=0.01 b3=2 Pays $1 b4=1

12. GSP and VCG • Google advertising its new auction:“… unique auction model uses Nobel Prize winning economic theory to eliminate … that feeling that you’ve paid too much” • GSP is a “new” auction, invented by Google. • Probably by mistake…. • But GSP is not VCG! • Not truthful! • Is it still efficient? (remember 1st-price auctions)

13. VCG prices b1=10 Slot 1 c1=0.08 Pays $5.625 Slot 2 b2=8 c2=0.03 Pays $1.67 Slot 3 c3=0.01 b3=2 Pays $1 b4=1

14. Outline • Introduction: online advertising • Sponsored search • Bidding and properties • Formal model • The Generalized second-price auction  Reminder: multi-unit auctions and VCG • Equilibrium analysis

15. Reminder • In an earlier class we discussed multi-unit auctions and VCG prices.

16. Auctions for non-Identical items • Non identical items: a, b, c, d, e, • Each bidder has a value for each itemvi(a),vi(b),bi(c),.. • Each bidder wants one item only.

17. Simultaneous Ascending Auction (sketch) • Start with zero prices. • Each bidder reports his favorite item • Price of over-demanded items is raised by $1. • Stop when there are no over-demanded items. • Bidders win their demands at the final prices. Claim: this auction terminates with: (1) Efficient allocation. (2) VCG prices ( ± $1 )

18. Market clearing prices • Conclusion: In a multi-unit auction with unit-demand bidders market-clearing prices exist. • And we saw that: • Such equilibrium exists. • these market clearing prices are exactly the VCG prices • the allocation is efficient • “market-clearing prices”: • every bidder receives his favorite item (given the prices) • all items are allocated (unless their price is 0).

19. Market clearing prices • “market-clearing prices”: • every bidder receives his favorite item (given the prices) • all items are allocated (unless their price is 0). “Envy-free” result: I don’t want Tinky-Winky’s item for the price that he pays. p4 p5 p1 p2 p3

20. Market clearing prices • And we saw that: • Market-clearing prices exist. • Easy to find: • Ascending-price auctions • VCG prices!!! • the allocation is always efficient • Again, an easy way to find market clearing prices: calculate VCG prices.

21. Sponsored search as multi-unit auction • Sponsored search can be viewed as multi-unit auction: • Each slot is an item • Advertiser i has value of ctvi for slot t. • We can conclude: In sponsored search auctions, the VCG prices are market-clearing prices. • No advertiser “envies” another advertiser and wants to have their slot+price. Slot 1 p1=5 I prefer “slot 1 + pay 5”to “slot 2 +pay 3” Slot 2 p2=3

22. Market Clearing Prices b1=10 Slot 1 c1=0.08 p1= $5.625 Slot 2 p2=$1.67 b2=8 c2=0.03 Slot 3 c3=0.01 p3= $1 b3=2 Let’s verify that Advertiser 1 do not want to switch to another slot under these prices: b4=1 u1(slot 1)= 0.08*(10-5.625) =0.35 u1(slot 2)= 0.03*(10-1.67) =0.25 u1(slot 3)= 0.01(10-1) =0.09

23. Equilibrium concept We will analyze the auction as a full-information game. Payoff are determined by the auction rules. Nash equilibrium: a set of bids in the GSP auction where no bidder benefits from changing his bid (given the other bids). Reason: equilibrium model “stable” bids in repeated-auction scenarios. (advertisers experiment…)

24. Equilibrium Let p1,..,pkbe market clearing prices. Let v1,…,vkbe the per-click values of the advertisers Claim: a Nash equilibrium is when each player i bids price pi-1 (bidder 1 can bid any number > p1). That is, each player bids the VCG price of the winner above them. Proof: Step 1: market-clearing prices are decreasing with slots. Step 2: show that this is an equilibrium.

25. Equilibrium bidding b1=10 The VCG prices Slot 1 c1=0.08 p1= $5.625 Slot 2 p2=$1.67 b2=8 c2=0.03 Slot 3 p3= $1 c3=0.01 b3=2 The following bids are an equilibrium: b1=6, b2=5.625, b3=1.67, b4=1 b4=1 First observation: the bids are decreasing. Is it always the case?

26. Step 1 • We will show:if p1,…,pkare market clearing prices then p1>p2>…>pk Slot j Utility: cj( vt– pj) ≥ Advertiser twins slot t: Slot t Utility: ct ( vt– pt ) Under the market clearing prices: t will not want to get slot j and pay pj. Since cj>ct, it must be that pt<pj.

27. Proof (cont.) Left to show:bidding as we proposed is a Nash equilibrium: • no bidder will benefit from deviating given the other bids. Claim: a Nash equilibrium is when each player i bids price pi-1 (bidder 1 can bid any number > p1).

28. Step 2: equilibrium • Let p1,…,pkbe market-clearing prices.bi=pi-1 , bi+1=pi , bi+2=pi+1 • Under GSP, i wins slot iand pays pi (=bi+1). • Should i lower his bid? If he bids below bi+1, he will win slot i+1 and pay pi+1. • Cannot happen under market –clearing prices. Slot i-1 bi Slot i bi+1 bi+2 Slot i+1

29. Equilibrium bidding b1=10 Slot 1 c1=0.08 p1= $5.625 Slot 2 p2=$1.67 b2=8 c2=0.03 Slot 3 p3= $1 c3=0.01 b3=2 The following bids are an equilibrium: b1=6, b2=5.625, b3=1.67, b4=1 b4=1

30. Step 2: equilibrium • Let p1,…,pkbe market-clearing prices.bi-2=pi-3 , bi-1=pi-2 , bi=pi-1 • Under GSP, i wins slot iand pays pi. • Should iincrease his bid? If he bids above bi-1, he will win slot i-1 and pay pi-2 (=bi-1) • But he wouldn’t change to slot i-1 even if he paid pi-1 (<pi-2). Slot i-1 bi-2 Slot i bi-1 Slot i+1 bi

31. Proof completed • We showed that the bids we constructed compose a Nash equilibrium in GSP. • In the equilibrium, bidder with higher values have higher bids. • GSP is efficient in equilibrium! • Many assumptions: no budgets, no brand advertisers, single-keyword market, clicks are all the same,…

32. Online advertising - Conclusion • Online advertising is a complex, multi-Billion dollar market environment. • With a rapidly increasing share of the advertising market. • These are environments that were, and still are, designed and created by humans. • Hard to evaluate the actual performance of new auction methods. • GSP is used by the large search engines.It is not truthful, but is efficient in equilibrium. • GSP is a new auction, invented by Google, probably by mistake…

33. Now let’s play…

34. 1. Party time

35. Balloons in the bag game • There are three balloons in the bag. • Either two blue and one red (“blue bag”) • Or one blue and two red (“red bag”) • There is a 50% chance of either majority • Each student in his turn will: • Take a balloon out of the bag, observe its color without telling the class. • Put ball back in bag. • After observing the ball, the student will guess whether the bag has blue/red majority. • How many students were right?

36. Analysis • The first student: • If observed blue, then “most chances” that we have blue majority, therefore a rational student will guess what he saw. • The second student: • Knows that the first student guessed what he saw. • Therefore, actually observes two draws from the bag. • If he also sees blue, say blue. If red, indifferent (let’s say he reports what he saw). • Third student: • Knows that the two previous students guessed what they observed. • If the first two students said blue, will also guess blue (even if he sees Red). • Fourth student: • If the first two guessed blue, the third does not tell anything. • will also guess blue (even if he sees Red).

37. Analysis • If the first two students said blue, the rational thing for every student to guess is blue. • With a red bag, 1/9 chance that the two first students will guess “blue” • And they are doing the right thing.

38. Meaning • The sequential nature of the game leads to scenarios where players ignore their private knowledge • Information is not aggregated • An inefficient outcome my be chosen. • “information cascade in social networks” – next class.

39. Examples • Choosing a restaurant • Looking at the sky • Fashion, going to a movie, voting

40. 2. Guess the average

41. Guess-the-average game • 10 students will receive notes with numbers • Keep secret from other students. • Goal: guess the average of the 10 numbers. • Each student with a note will write a guess on a note. • The closest bid to the average wins.