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Auction Theory

Auction Theory. Class 9 – Online Advertising. Outline. Part 1: Bla bla bla Part 2: Equilibrium analysis of Google’s auction. Outline. Introduction: online advertising Sponsored search Bidding and properties Formal model The Generalized second-price auction

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Auction Theory

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  1. Auction Theory Class 9 – Online Advertising

  2. Outline Part 1: Blablabla Part 2: Equilibrium analysis of Google’s auction

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

  4. Classic advertising

  5. Classic advertising: newspapers

  6. Classic advertising: TV

  7. Classic advertising: Billboards

  8. Online advertising

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

  10. Sponsored search

  11. Semantic advertising

  12. Email advertising

  13. 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)

  14. 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.

  15. Advertising types • Brand advertisers • Direct advertisers

  16. 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

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

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

  19. Sponsored search auctions Search keywords keywords keywords Ad slots

  20. Bidding • 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.

  21. Bidding: more details 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.

  22. Economics of sponsored search Search engines Internet users advertisers

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

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

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

  26. 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) :

  27. 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*0.08 + 8*0.03 + 2*0.01

  28. 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.

  29. 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

  30. Pay-your-bid data (14 hours)

  31. Pay-your-bid data (week)

  32. 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?

  33. 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…

  34. 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.

  35. 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

  36. 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)

  37. Example: GSP not truthful v1=10 Slot 1 c1=0.08 Slot 2 v2=8 c2=0.03 Slot 3 c3=0.01 v3=2 wins slot 1. utility: 0.08 * (10-8) = 0.16 b1=10 wins slot 2.utility: 0.3 * (8-2) = 0.18 b1=5

  38. 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 Expected welfare of the others (1 participates): 8*0.03 + 2*0.01 = 0.26 Expected welfare of the others (without 1):8*0.08 + 2*0.03 + 1*0.01 = 0.71 VCG payment for bidder 1 (expected): 0.71 - 0.26 = 0.45 VCG payment for bidder 1 (per click): 0.45/0.08 = 5.625 Pays $1 b4=1

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

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

  41. 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.

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

  43. Walrasian Equilibrium For a bidder i, and prices p1,…,pnwe say that the bundle T is a demand of i if for every other bundle S: • A Walrasian equilibrium is an allocation S1,…,Snand item prices p1,…,pnsuch that: • Si is the demand of bidder i under the prices p1,…,pn • For any item j that is not allocated (not in S1,…,Sn) we have pj=0

  44. Market clearing prices • 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.

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

  46. 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. • allocation is “envy free” Slot 1 p1=5 I prefer “slot 1 + pay 5”to “slot 2 +pay 3” Slot 2 p2=3

  47. Market Clearing 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 p1= $5.625 p2=$1.67 p3= $1 Pays $1 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

  48. 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…)

  49. GSP is efficient 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.

  50. 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). Proof: Step 1: show that market-clearing prices are decreasing with slots. Step 2: show that this is an equilibrium.

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