libeccio.di.unisa.itlibeccio.di.unisa.it/SocialNetworks_2015/slide/sponsored_search.pdf ·...

Sponsored Search

Sponsored Search

Keyword Advertising

The Web Search approach

I Keyword-Based AdvertisingI Pay-per-Click

Pay-per-Impression

I Ads not relevant to the pageI Pay even if ad is not useful

Does it work?

I The top spot for calligraphy pens costs $1.50I The top spot for calligaphy pens costs $0.60I The top spot for loan consolidation costs $50

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Sponsored Search

Keyword Advertising



Pay-per-ImpressionI Ads not relevant to the page

I Pay even if ad is not useful

Does it work?


2

Sponsored Search

Keyword Advertising



Pay-per-ImpressionI Ads not relevant to the pageI Pay even if ad is not useful

Does it work?


2

Sponsored Search

Keyword Advertising

The Web Search approachI Keyword-Based Advertising

I Pay-per-Click


Does it work?


2

Sponsored Search

Keyword Advertising

The Web Search approachI Keyword-Based AdvertisingI Pay-per-Click


Does it work?


2

Sponsored Search

Keyword Advertising



Does it work?I The top spot for calligraphy pens costs $1.50I The top spot for calligaphy pens costs $0.60

I The top spot for loan consolidation costs $50

2

Sponsored Search

Keyword Advertising



Does it work?I The top spot for calligraphy pens costs $1.50I The top spot for calligaphy pens costs $0.60I The top spot for loan consolidation costs $50

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Sponsored Search

How the prices are chosen?

Preliminary definitionsI Clickthrough rates rj of spot j

I Clickthrough rates are knownI Clickthrough rates do not depend on ad quality or relevanceI Clickthrough rates do not depend on ads on other slots

I Revenue per click vi for advertiser iI Advertiser i expected welfare from slot j = vi rj

I This is the maximum amount i is willing to pay for jI Goal: To maximize social welfare

I Best spot to the best advertiser, second best spot to secondbest advertiser, . . .

Problem: we do not know who is the best advertiser

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Sponsored Search




I Revenue per click vi for advertiser i

I Advertiser i expected welfare from slot j = vi rjI This is the maximum amount i is willing to pay for j

I Goal: To maximize social welfareI Best spot to the best advertiser, second best spot to second

best advertiser, . . .


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Sponsored Search





I This is the maximum amount i is willing to pay for j

I Goal: To maximize social welfareI Best spot to the best advertiser, second best spot to second

best advertiser, . . .


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Sponsored Search





I This is the maximum amount i is willing to pay for jI Goal: To maximize social welfare

I Best spot to the best advertiser, second best spot to secondbest advertiser, . . .


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Sponsored Search

How can we solve this problem?

TruthfulnessI Each advertiser i submit a bid biI It is a dominant strategy for an advertiser i to bid truthfully,

i.e. bi = vi

Can we run second price auctions?I They have been defined for single item auctionsI Now we have multiple slots to sell

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Sponsored Search

Second Price Auctions revisitedI The item is allocated to the

highest bidder

I The winner is charged thesecond highest bid

lent tothe harm her presencecauses to the other bidders

I Allocation maximizes thesocial welfare (w.r.t. bids)

I Any agent is charged anamount that is equivalent tothe harm her presencecauses to the other biddersExamples

I n agents with valuation v1 ≥ · · · ≥ vn

I If agent 1 is in the auctionI she wins the itemI remaining player have utility 0

I If agent 1 is not in the auctionI agent 2 wins the item and has utility v2I remaining player have utility 0

I The harm caused by agent 1 amounts to v2

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Sponsored Search


highest bidderI The winner is charged the

second highest bid








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Sponsored Search



second highest bid



I Any agent is charged anamount that is equivalent tothe harm her presencecauses to the other bidders

ExamplesI n agents with valuation v1 ≥ · · · ≥ vn




5

Sponsored Search



second highest bid








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second highest bid




I n agents with valuation v1 ≥ · · · ≥ vnI If agent 1 is in the auction

I she wins the itemI remaining player have utility 0



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Sponsored Search

VCG Auctions

Vickrey-Clarke-Groves PrincipleI Agents submit bidsI Allocation maximizes the social welfareI Prices are the harm to other bidders

VCG PricesI SW (A) = maximum social welfare with all bidders and slotsI SW (A−i

−j) = maximum social welfare without j and its slot iI SW (A−j) = maximum social welfare without j (but all slots)

pij = SW (A−j) − SW (A−i−j)

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuations

I Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)

I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12

I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25

I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13

I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32

I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35

I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3

I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40

I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40

I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VGC Auctions - ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuationsI Optimal assignment (welfare = 42)I Welfare without first advertiser and first slot: 12I Welfare without first advertiser but with first slot: 25I The first advertiser must pay 25 − 12 = 13I Welfare without second advertiser and second slot: 32I Welfare without the second advertiser but with second slot: 35I The second advertiser must pay 35 − 32 = 3I Welfare without third advertiser and third slot: 40I Welfare without the third advertiser but with third slot: 40I The third advertiser must pay 40 − 40 = 0

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Sponsored Search

VCG Auctions: Truthfulness

I If the lie does not affect the assigned slot, payoff unchangedI By lying, i takes item k in place of item j

vij − pij?≥ vih − pih

vij −[SW (A−i ) − SW (A−j

−i )] ?

≥ vih −[SW (A−i ) − SW (A−h

−i )]

vij + SW (A−j−i )

?≥ vih + SW (A−h

−i )

SW (A)?≥ vih + SW (A−h

−i )

YES

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Sponsored Search


I If the lie does not affect the assigned slot, payoff unchanged

I By lying, i takes item k in place of item j



−i )] ?


−i )]



−i )


−i )

YES

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Sponsored Search





−i )] ?


−i )]



−i )


−i )

YES

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Sponsored Search





−i )] ?


−i )]



−i )


−i ) YES

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Sponsored Search

VGC Auctions: Market Clearing PricesVGC pricesPersonalized Prices

Market Clearing pricesPosted Prices

Let us model sponsored search as Matching Markets

x3 x30, 15, 6 3

y2 y20, 10, 4 2

z1 z10, 5, 2 1

1 101 10 13

2 52 5 3

3 23 2 0

VCG prices vs. Market Clearing PricesVCG prices are market clearing prices of minimum total sum

ObservationsI VGC Auctions are a generalization of Second-Price Auctions

I Market-clearing prices given by generalized ascending auctionsI Ascending Auctions are equivalent to Second-Price Auctions

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Sponsored Search



Let us model sponsored search as Matching Marketsx3

x30, 15, 6 3

y2

y20, 10, 4 2

z1

z10, 5, 2 1

1 10

1 10 13

2 5

2 5 3

3 2

3 2 0




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Sponsored Search




x3

x30, 15, 6 3

y2

y20, 10, 4 2

z1

z10, 5, 2 1

1 10

1 10 13

2 5

2 5 3

3 2

3 2 0




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Sponsored Search




x3

x30, 15, 6 3

y2

y20, 10, 4 2

z1

z10, 5, 2 1

1 10

1 10 13

2 5

2 5 3

3 2

3 2 0


ObservationsI VGC Auctions are a generalization of Second-Price AuctionsI Market-clearing prices given by generalized ascending auctions

I Ascending Auctions are equivalent to Second-Price Auctions

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Sponsored Search




x3

x30, 15, 6 3

y2

y20, 10, 4 2

z1

z10, 5, 2 1

1 10

1 10 13

2 5

2 5 3

3 2

3 2 0


ObservationsI VGC Auctions are a generalization of Second-Price AuctionsI Market-clearing prices given by generalized ascending auctionsI Ascending Auctions are equivalent to Second-Price Auctions

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Sponsored Search

VCG Auctions: Advantages and Drawbacks

AdvantagesI TruthfulnessI Market Clearing PriceI The approach extend to other types of auctions

DrawbacksI Payment rule is hard to describeI It may be expensive to compute paymentsI It maximizes social welfare, but what about revenue?

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Sponsored Search



DrawbacksI Payment rule is hard to describe

I It may be expensive to compute paymentsI It maximizes social welfare, but what about revenue?

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Sponsored Search



DrawbacksI Payment rule is hard to describeI It may be expensive to compute payments

I It maximizes social welfare, but what about revenue?

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Sponsored Search



DrawbacksI Payment rule is hard to describeI It may be expensive to compute paymentsI It maximizes social welfare, but what about revenue?

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Sponsored Search

Generalized Second Price AuctionVCG Auction

I Agents submit bidsI Allocation maximizes the

social welfareI Prices are the harm to other

bidders

GSP Auction


social welfareI Price is the valuation of the

next slot winnerExample

I 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuations

I The first advertiser pays 2 × 10 = 20 for the first slotI The second advertiser pays 1 × 5 = 5 for the second slotI The third advertiser pays 0 × 2 = 0 for the third slot

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Sponsored Search


I Agents submit bids

I Allocation maximizes thesocial welfare

I Prices are the harm to otherbidders

GSP Auction






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Sponsored Search


I Agents submit bids



GSP AuctionI Agents submit bids


I Price is the valuation of thenext slot winner

ExampleI 3 slots with Clickthrough Rates 10, 5 and 2I 3 advertisers with Revenue per Click 3, 2 and 1I Assume bids = valuations


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Sponsored Search



social welfare


GSP AuctionI Agents submit bids





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Sponsored Search



social welfare


GSP AuctionI Agents submit bidsI Allocation maximizes the

social welfare




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Sponsored Search




bidders


social welfare




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Sponsored Search




bidders



next slot winner



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Sponsored Search



I There may be multiple equilibriaI Bids bx = 5, by = 4, bz = 2 are in equilibrium

I Bids bx = 3, by = 5, bz = 1 are in equilibriumI There are equilibria that do not maximize the social welfareI There are equilibria with revenue larger than the VCG revenue



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I There are equilibria that do not maximize the social welfare

I There are equilibria with revenue larger than the VCG revenueI (bx = 5, by = 4, bz = 2) gives revenue 48I Truthful equilibrium gives revenue 44


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I (bx = 5, by = 4, bz = 2) gives revenue 48

I Truthful equilibrium gives revenue 44I There are equilibria with revenue lower than the VCG revenue


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I There are equilibria with revenue lower than the VCG revenue


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Sponsored Search

GSP AuctionDoes an equilibrium exists?

I Sponsored Search as a Matching MarketI Compute bids from Market Clearing Prices

x7 x70, 28 7 x70, 28, 0 7

y6 y60, 24 6 y60, 24, 0 6

z1 z10, 4 1 z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibrium

I Lower bid and same slot

NO

I Lower bid and lower slot

NO

I Higher bid and same slot

NO

I Higher bid and higher slot

NO

I Assigned: There are equilibria with good properties

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Sponsored Search


I Sponsored Search as a Matching Market

I Compute bids from Market Clearing Pricesx7 x70, 28 7 x70, 28, 0 7

y6 y60, 24 6 y60, 24, 0 6

z1 z10, 4 1 z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



I Compute bids from Market Clearing Prices

x7

x70, 28 7 x70, 28, 0 7

y6

y60, 24 6 y60, 24, 0 6

z1

z10, 4 1 z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



I Compute bids from Market Clearing Pricesx7

x70, 28 7

x70, 28, 0 7

y6

y60, 24 6

y60, 24, 0 6

z1

z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



I Compute bids from Market Clearing Pricesx7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0 xb∗1 > 4 70, 28, 0

y60, 24, 0 yb∗2 = 4 60, 24, 0

z10, 4, 0 zb∗3 = 1 10, 4, 0

1 401 40 p∗1 = 4

2 42 4 p∗2 = 1

3 03 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n



NO


NO


NO


NO


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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibriumI Lower bid and same slot

NO


NO


NO


NOI Assigned: There are equilibria with good properties

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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibriumI Lower bid and same slot NOI Lower bid and lower slot

NO


NO



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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibriumI Lower bid and same slot NOI Lower bid and lower slot NOI Higher bid and same slot

NO



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Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibriumI Lower bid and same slot NOI Lower bid and lower slot NOI Higher bid and same slot NOI Higher bid and higher slot


13

Sponsored Search



x7 x70, 28 7

x70, 28, 0 7

y6 y60, 24 6

y60, 24, 0 6

z1 z10, 4 1

z10, 4, 0 1

1 10

2 4

3 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

x70, 28, 0

xb∗1 > 4 70, 28, 0

y60, 24, 0

yb∗2 = 4 60, 24, 0

z10, 4, 0

zb∗3 = 1 10, 4, 0

1 40

1 40 p∗1 = 4

2 4

2 4 p∗2 = 1

3 0

3 0 p∗3 = 0

p∗1 ≥ p∗

2 ≥ . . . ≥ p∗n

I These bids are in equilibriumI Lower bid and same slot NOI Lower bid and lower slot NOI Higher bid and same slot NOI Higher bid and higher slot NO


13

Sponsored Search

Ad Quality

I We assumed that the Clickthrough Rate depends only on slot

I High quality ads attract more clicks (and larger revenue)I Embedding ad quality in the Sponsored Search model

I Each ad has a quality factor qjI Clickthrough Ratio of ad j in slot i : qj riI Advertiser j valuation for slot i : vij = vjqj ri

I This change does not affect the properties of auctions

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Sponsored Search

Ad Quality

I We assumed that the Clickthrough Rate depends only on slotI High quality ads attract more clicks (and larger revenue)

I Embedding ad quality in the Sponsored Search modelI Each ad has a quality factor qjI Clickthrough Ratio of ad j in slot i : qj riI Advertiser j valuation for slot i : vij = vjqj ri


14

Sponsored Search

Ad Quality


I Embedding ad quality in the Sponsored Search model

I Each ad has a quality factor qjI Clickthrough Ratio of ad j in slot i : qj riI Advertiser j valuation for slot i : vij = vjqj ri


14

Sponsored Search

Ad Quality


I Embedding ad quality in the Sponsored Search modelI Each ad has a quality factor qj

I Clickthrough Ratio of ad j in slot i : qj riI Advertiser j valuation for slot i : vij = vjqj ri


14

Sponsored Search

Ad Quality


I Embedding ad quality in the Sponsored Search modelI Each ad has a quality factor qjI Clickthrough Ratio of ad j in slot i : qj ri

I Advertiser j valuation for slot i : vij = vjqj ri


14

Sponsored Search

Ad Quality


I Embedding ad quality in the Sponsored Search modelI Each ad has a quality factor qjI Clickthrough Ratio of ad j in slot i : qj riI Advertiser j valuation for slot i : vij = vjqj ri


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