Auction Theory

Class 9 – Online Advertising

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Outline

Part 1: Bla bla bla

Part 2: Equilibrium analysis of Google’s auction

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Outline1. Introduction: online advertising

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

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Classic advertising

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Classic advertising: newspapers

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Classic advertising: TV

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Classic advertising: Billboards

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Online advertising

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Banner ads1. General:

1. Examples: banner, sponserd search, video, videa games, adsense, in social networks

2. Some numbers3. advantages over classic ads4. Ppi,ppc,ppconversion

2. Sponsored search:1. Some history2. Definitions: ctr, conversion-rate3. GSP- definition, non truthfulness.4. Diagram of first-price yahoo data.5. Analysis of equilibrium.

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Sponsored search

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Semantic advertising

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Email advertising

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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)

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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.

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Advertising types• Brand advertisers

• Direct advertisers

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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

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Outline1. Introduction: online advertising

Sponsored search– Bidding and properties– Formal model– The Generalized second-price auction– Reminder: multi-unit auctions and VCG– Equilibrium analysis

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Sponsored search auctions

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Real (“organic”) search result Ads: “sponsored search”

Sponsored search auctions

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Search keywords keywordskeywordsAd slots

Bidding

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• 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 details

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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

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Internet usersSearch engines

advertisers

Click Through Rates

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• Are all ads equal?

• Position matters.– User mainly click on top ads.

• Need to understand user behavior.

Click Through rate

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9%4%

2%

0.5%

0.2%

0.08%

Click Through rate

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c1

c2

c3

c4

…

…

ck

Formal model

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• 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) :

k

iiivc

1

Example

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v1=10

v2=8

v3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

The efficient outcome:

Total efficiency: 10*0.08 + 8*0.03 + 2*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

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Pay-your-bid data (14 hours)

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Pay-your-bid data (week)

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Unstable biddingThink 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?

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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…

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GSP

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• 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.

Example

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b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

Pays $8

Pays $2

b4=1

Pays $1

GSP and VCG

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• 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)

Example: GSP not truthful

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v1=10

v2=8

v3=2

c1=0.08

c2=0.03

c3=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

b1=10

b1=5

VCG prices

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b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

Pays $5.625

Pays $1.67

b4=1

Pays $1Expected 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

Outline1. Introduction: online advertising

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

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Reminder

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• 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 itemvi(a),vi(b),bi(c),..

• Each bidder wants one item only.

Auctions for non-Identical items

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Simultaneous Ascending Auction1. 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.

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Claim: this auction terminates with:(1) Efficient allocation. (2) VCG prices ( ± $1 )

Walrasian Equilibrium• For a bidder i, and prices p1,…,pn we say that the

bundle T is a demand of i if for every other bundle S:

Sj

jiTj

ji pSvpTv )()(

• A Walrasian equilibrium is an allocation S1,…,Sn and item prices p1,…,pn such 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

Market clearing prices

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• 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

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• 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

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• 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 1Slot 2p2=3

p1=5I prefer “slot 1 + pay 5”to “slot 2 +pay 3”

Market Clearing Prices

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b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

Pays $5.625

Pays $1.67

b4=1

Pays $1 p1= $5.625 p2=$1.67 p3= $1

u1(slot 1)= 0.08*(10-5.625) =0.35u1(slot 2)= 0.03*(10-1.67) =0.25u1(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

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We will analyze the auction as a full-information game.b2=1 b2=2 b3=3 ….

b1=1b1=2b1=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

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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

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Let p1,..,pk be market clearing prices.

Let v1,…,vk be 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.

Equilibrium bidding

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b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

b4=1

p1= $5.625 p2=$1.67 p3= $1

The following bids are an equilibrium:b1=6, b2=5.625, b3=1.67, b4=1

First observation: the bids are decreasing. Is it always the case?

Step 1

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• We will show:if p1,…,pk are market clearing prices then p1>p2>…>pk

Slot j

Slot tUtility: ct ( vt – pt )

Utility: cj ( vt – pj )

Advertiser t wins slot t:

Market clearing prices: t will not want to get slot j and pay pj.

Since cj>ct, it must be that pt<pj.

≥ (j<t)

Step 2: equilibrium

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• Under GSP, i wins slot i and pays pi.

• 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

Slot i+1

Slot i-1

• Let p1,…,pk be market-clearing prices.

bi-1=pi-2 , bi=pi-1 , bi+1=pi

bi

bi+1

bi+2

Equilibrium bidding

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b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

b4=1

p1= $5.625 p2=$1.67 p3= $1

The following bids are an equilibrium:b1=6, b2=5.625, b3=1.67, b4=1

Step 2: equilibrium

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• Under GSP, i wins slot i and pays pi.

• Should i increase 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

Slot i+1

Slot i-1

• Let p1,…,pk be market-clearing prices.

bi-1=pi-2 , bi=pi-1 , bi+1=pi

bi-2

bi

bi-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!

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Another example

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• Let’s consider a 2-slot case, so we can present the solution graphically.

b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

Another example

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• 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:

• p1,p2 ≥ 2– Bidder 2 prefers slot 2:

• 0.04*(8-p2) ≥ 0.08*(8-p1) p1 ≥ p2/2 - 4– Bidder 1 prefers slot 1:

• 0.08*(10-p1) ≥ 0.04*(10-p2) p1 ≤ p2/2 - 5

b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

Another example

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b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

2

4

5

2

The set of all Walrasian price

vectors

p1 ≤ p2/2 - 5

p1 ≥ p2/2 - 4

p1,p2 ≥ 2p1

p2

Another example

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• What are the VCG prices?p1 = (8*0.08+2*0.04-8*0.04)/0.08 = 5

p2 = (2*0.04)/0.04 = 2

b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

Another example

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b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

2

4

5

2

VCG prices

Recall: with unit-demand preferences, VCG prices are the lowest Walrasian prices

p1 ≤ p2/2 - 5

p1 ≥ p2/2 - 4

p1,p2 ≥ 2p1

p2

Another example

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• What are the GSP prices?

p1 > 5

p2 = (2*0.04)/0.04 = 2

b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

Another example

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b1=10

b2=8

b3=2

c1=0.08

c2=0.04

Slot 1

Slot 2

2

4

5

2

GSP prices

Total revenue is greater than in VCG

p1 ≤ p2/2 - 5

p1 ≥ p2/2 - 4

p1,p2 ≥ 2p1

p2

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…

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