Auction Theory Class 9 – Online Advertising 1

Outline Part 1: Bla bla bla Part 2: Equilibrium analysis of Google’s auction 2

Outline 1.Introduction: online advertising 2.Sponsored search – Bidding and properties – Formal model – The Generalized second-price auction – Reminder: multi-unit auctions and VCG – Equilibrium analysis 3

Classic advertising 4

Classic advertising: newspapers 5

Classic advertising: TV 6

Classic advertising: Billboards 7

Online advertising 8

Banner ads 1.General: 1.Examples: banner, sponserd search, video, videa games, adsense, in social networks 2.Some numbers 3.advantages over classic ads 4.Ppi,ppc,ppconversion 2.Sponsored search: 1.Some history 2.Definitions: ctr, conversion-rate 3.GSP- definition, non truthfulness. 4.Diagram of first-price yahoo data. 5.Analysis of equilibrium. 9

Sponsored search 10

Semantic advertising 11

advertising 12

Online Advertising: Some rough numbers 2008: – Worldwide advertising spending: about 500 Billion – Online advertising: about 10% of that (!!!!) Google : over 98% of revenue from advertising (Total $21 Billion in 2008) Double digit growth in online advertising in the past and in the near future (expected) 13

Online advertising - advantages Targeting – By search keywords, context, – Personalized ads. Additional information – Time, history, personal data Advanced billing/effectiveness options – By eyeballs, clicks, actual purchases – “pay only when you sell” Advanced bidding options – No printing/”menu” costs. Variety of multimedia tools Enables cheap campaigns, low entry levels. 14

Advertising types Brand advertisers Direct advertisers 15

Revenue model Pay per impression – CPM- cost per mille. Cost per thousand impressions. – Good for brand advertisers Pay per click – CPC - cost per click. – Most prevalent – Brand advertisers get value for free. Pay per action – CPA – cost per action/acquisition/conversion. – Risk-free for advertisers – Harder to implement 16

Outline 1.Introduction: online advertising  Sponsored search – Bidding and properties – Formal model – The Generalized second-price auction – Reminder: multi-unit auctions and VCG – Equilibrium analysis 17

Sponsored search auctions 18 Real (“organic”) search result Ads: “sponsored search”

Sponsored search auctions 19 Search keywordskeywords Ad slots

Bidding 20 A basic campaign for an advertiser includes: Some keywords have bids greater than $50 – E.g., Mesothelioma Search engine provides assistance traffic estimator, keyword suggestions, automatic bidding Google started (and stopped) pay-per-action sales. List of : keywords + bid per click “hotel Las Vegas” $5 “Nikon camera d60” $30 Budget (for example, daily) I want to spend at most $500 a day

Bidding: more detailsmore details 21 When does a keyword match a user search-query? – When bidding $5 per “hotel California”. Will “hotel California song” appear? Broad match – California hotel, hotel California Hilton, cheap hotel California. Exact match: – “ hotel California” with no changes or additions. Negative words: – “ hotel California –song -eagles “ Many more options: – Geography, time, languages, mobile/desktops/laptops, etc.

Economics of sponsored search 22 Internet users Search engines advertisers

Click Through Rates 23 Are all ads equal? Position matters. – User mainly click on top ads. Need to understand user behavior.

Click Through rate 24 9% 4% 2% 0.5% 0.2% 0.08%

Click Through rate 25 c1c1 c2c2 c3c3 c4c4 … … ckck

Formal model 26 n advertisers For advertiser i: value per click v i k ad slots (positions): 1,…,k Click-through-rates: c 1 > c 2 > …> c k – Simplifying assumption: CTR identical for all users. Advertiser i, wins slot t, pays p. utility: c t (v i –p) Social welfare (assume advertisers 1,..,k win slots 1,…,k) :

Example 27 v 1 =10 v 2 =8 v 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 The efficient outcome: Total efficiency: 10* * *0.01

Brief History of Sponsored Search Auctions (Slide: Jon Levin) Pre-1994: advertising sold on a per-impression basis, traditional direct sales to advertisers. 1994: Overture (then GoTo) allows advertisers to bid for keywords, offering some amount per click. Advertisers pay their bids. Late 1990s: Yahoo! and MSN adopt Overture, but mechanism proves unstable - advertisers constantly change bids to avoid paying more than necessary. 2002: Google modifies keyword auction to have advertisers pay minimum amount necessary to maintain their position (i.e. GSP)- followed by Yahoo! and MSN.

How would you sell the slots? Yahoo! (that acquired Overture) sold ads in a pay-your- bid auction (that is, first-price auction). Results: Sawtooth 29

Pay-your-bid data (14 hours) 30

Pay-your-bid data (week) 31

Unstable bidding Think about two neighboring gas stations. What’s bad with instability? Inefficiency – advertisers with high values spend part of the time on the top. Investment in strategy – advertisers invest a lot of efforts (time, software, consultants, etc.) handling their strategy. Relevance – assuming advertisers’ values are correlated with their relevance, bidders see less relevant ads. Is there an efficient auction then? 32

Why efficiency? Isn’t Google (and other internet companies) required by their shareholders to maximize profit? Reasons: – Long term thinking in a competitive environment. – Making the whole pie larger. – Easier to model and analyze… 33

GSP 34 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 b i – The ith highest bidder wins the ith slot and pays the (i+1)th highest bid. With one slot: reduces to 2 nd -price auction.

Example 35 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 Pays $8 Pays $2 b 4 =1 Pays $1

GSP and VCG 36 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 1 st -price auctions)

Example: GSP not truthful 37 v 1 =10 v 2 =8 v 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 wins slot 1. utility: 0.08 * (10-8) = 0.16 wins slot 2. utility: 0.3 * (8-2) = 0.18 b 1 =10 b 1 =5

VCG prices 38 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 Pays $5.625 Pays $1.67 b 4 =1 Pays $1 Expected welfare of the others (1 participates): 8* *0.01 = 0.26 Expected welfare of the others (without 1): 8* * *0.01 = 0.71 VCG payment for bidder 1 (expected): = 0.45 VCG payment for bidder 1 (per click): 0.45/0.08 = 5.625

Outline 1.Introduction: online advertising 2.Sponsored search – Bidding and properties – Formal model – The Generalized second-price auction  Reminder: multi-unit auctions and VCG – Equilibrium analysis 39

Reminder 40 In the previous class we discussed multi-unit auctions and VCG prices.

Non identical items: a, b, c, d, e, Each bidder has a value for each item v i (a),v i (b),b i (c),.. Each bidder wants one item only. Auctions for non-Identical items 41

Simultaneous Ascending Auction 1.Start with zero prices. 2.Each bidder reports her favorite item  Provisional winners are announced. 3.Price of over-demanded items is raised by $1.  Following bids by losing bidders. 4.Stop when there are no over-demanded items. – Provisional winners become winners. 42 Claim: this auction terminates with: (1) Efficient allocation. (2) VCG prices ( ± $1 )

Walrasian Equilibrium For a bidder i, and prices p 1,…,p n we say that the bundle T is a demand of i if for every other bundle S: A Walrasian equilibrium is an allocation S 1,…,S n and item prices p 1,…,p n such that: – S i is the demand of bidder i under the prices p 1,…,p n – For any item j that is not allocated (not in S 1,…,S n ) we have p j =0

Market clearing prices 44 We saw: In a multi-unit auction with unit-demand bidders: – VCG prices are market-clearing prices Not true for more general preferences – The allocation supported by market clearing prices (Walrasian equilibrium) is efficient. Always true – The simultaneous ascending auction terminates with VCG prices And thus with an efficient allocation and market-clearing prices.

Market clearing prices 45 Another interpretation of market-clearing prices: envy-free prices. No bidder “envies” another bidder and wants to have their item + price instead oh hers.

Sponsored search as multi-unit auction 46 Sponsored search can be viewed as multi-unit auction: – Each slot is an item – Advertiser i has value of c t v i for slot t. We can conclude: In sponsored search auctions, the VCG prices are market-clearing prices. – allocation is “envy free” Slot 1 Slot 2 p 2 =3 p 1 =5 I prefer “slot 1 + pay 5” to “slot 2 +pay 3”

Market Clearing Prices 47 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 Pays $5.625 Pays $1.67 b 4 =1 Pays $1 p 1 = $5.625p 2 =$1.67 p 3 = $1 u 1 (slot 1)= 0.08*( )=0.35 u 1 (slot 2)= 0.03*( )=0.25 u 1 (slot 3)= 0.01(10-1)=0.09 Let’s verify that Advertiser 1 do not want to switch to another slot under these prices:

Equilibrium concept 48 We will analyze the auction as a full-information game. b 2 =1b 2 =2b 3 =3…. b 1 =1 b 1 =2 b 1 =3 … Payoff are determined by the auction rules. Reason: equilibrium model “stable” bids in repeated- auction scenarios. (advertisers experiment…) Nash equilibrium: a set of bids in the GSP auction where no bidder benefits from changing his bid (given the other bids).

GSP is efficient 49 Next slides: we will prove that the GSP auction is efficient. – although not truthful – That is, there is an equilibrium (in the complete- information game) for which the allocation is efficient. (there might be other equilibria that may be inefficient) Way of proof: we will use the VCG prices to define the equilibrium in the auction.

Equilibrium 50 Let p 1,..,p k be market clearing prices. Let v 1,…,v k be the per-click values of the advertisers Claim: a Nash equilibrium is when each player i bids price p i-1 (bidder 1 can bid any number > p 1 ). Proof: Step 1: show that market-clearing prices are decreasing with slots. Step 2: show that this is an equilibrium.

Equilibrium bidding 51 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 b 4 =1 p 1 = $5.625p 2 =$1.67 p 3 = $1 The following bids are an equilibrium: b 1 =6, b 2 =5.625, b 3 =1.67, b 4 =1 First observation: the bids are decreasing. Is it always the case?

Step 1 52 We will show: if p 1,…,p k are market clearing prices then p 1 >p 2 >…>p k Slot j Slot t Utility: c t ( v t – p t ) Utility: c j ( v t – p j ) Advertiser t wins slot t: Market clearing prices: t will not want to get slot j and pay p j. Since c j >c t, it must be that p t <p j. (j<t)

Step 2: equilibrium 53 Under GSP, i wins slot i and pays p i. Should i lower his bid? If he bids below b i+1, he will win slot i+1 and pay p i+1. – Cannot happen under market – clearing prices. Slot i Slot i+1 Slot i-1 Let p 1,…,p k be market-clearing prices. b i-1 =p i-2, b i =p i-1, b i+1 =p i bibi b i+1 b i+2

Equilibrium bidding 54 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.03 c 3 =0.01 Slot 1 Slot 2 Slot 3 b 4 =1 p 1 = $5.625p 2 =$1.67 p 3 = $1 The following bids are an equilibrium: b 1 =6, b 2 =5.625, b 3 =1.67, b 4 =1

Step 2: equilibrium 55 Under GSP, i wins slot i and pays p i. Should i increase his bid? If he bids above b i-1, he will win slot i-1 and pay p i-2 (=b i-1 ) – But he wouldn’t change to slot i-1 even if he paid p i-1 (<p i-2 ). Slot i Slot i+1 Slot i-1 Let p 1,…,p k be market-clearing prices. b i-1 =p i-2, b i =p i-1, b i+1 =p i b i-2 bibi b i-1

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. Auction is efficient in equilibrium! 56

Another example 57 Let’s consider a 2-slot case, so we can present the solution graphically. b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot 2

Another example 58 Let p1,p2 be per-click prices. What are the Walrasian equilibria in this auction? (Reminder, each bidder should get his demand) – Bidder 3 should not demand any item: p 1,p 2 ≥ 2 – Bidder 2 prefers slot 2: 0.04*(8-p 2 ) ≥ 0.08*(8-p 1 )  p 1 ≥ p 2 /2 - 4 – Bidder 1 prefers slot 1: 0.08*(10-p 1 ) ≥ 0.04*(10-p 2 )  p 1 ≤ p 2 /2 - 5 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot 2

Another example 59 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot The set of all Walrasian price vectors p 1 ≤ p 2 /2 - 5 p 1 ≥ p 2 /2 - 4 p 1,p 2 ≥ 2 p1p1 p2p2

Another example 60 What are the VCG prices? p 1 = (8*0.08+2*0.04-8*0.04)/0.08 = 5 p 2 = (2*0.04)/0.04 = 2 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot 2

Another example 61 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot VCG prices Recall: with unit-demand preferences, VCG prices are the lowest Walrasian prices p 1 ≤ p 2 /2 - 5 p 1 ≥ p 2 /2 - 4 p 1,p 2 ≥ 2 p1p1 p2p2

Another example 62 What are the GSP prices? p 1 > 5 p 2 = (2*0.04)/0.04 = 2 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot 2

Another example 63 b 1 =10 b 2 =8 b 3 =2 c 1 =0.08 c 2 =0.04 Slot 1 Slot GSP prices Total revenue is greater than in VCG p 1 ≤ p 2 /2 - 5 p 1 ≥ p 2 /2 - 4 p 1,p 2 ≥ 2 p1p1 p2p2 VCG

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… 64