Mechanism Design for InternetAdvertisting

Philip Zigoris

UC Santa Cruz

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Introduction

What is mechanism design?

Why is this setting different than what we’ve been talk-

ing about?

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OverviewPart I:

• What are some different types of auctions?• Does it pay to misrepresent yourself?• What happens if the bidding is done by a computerized

agent?

(Varian, H.Economic Mechanism Design for Computerized Agents.)

Part II:

• How does internet advertising work? More appropriately,

what is our model of internet advertising?• Is it fair? Whose interest does it favor?• How does it compare to standard auction methods?

(Edelman, B. et al.Internet Advertising and the Generalized Second Price Auction: Selling Bil-

lions of Dollars Worth of Keywords.) Mechanism Design for Internet Advertisting – p.3/22

Part I

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Different Types of AuctionsEnglish Auction Open bidding with increasing price.

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Different Types of AuctionsEnglish Auction Open bidding with increasing price.

Dutch Auction Price is lowered until someoneaccepts.

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Different Types of AuctionsEnglish Auction Open bidding with increasing price.

Dutch Auction Price is lowered until someoneaccepts.

Sealed First Price Auction Every submits their bidin secret. Highest bidder pays the amount theybid.

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Different Types of AuctionsEnglish Auction Open bidding with increasing price.

Dutch Auction Price is lowered until someoneaccepts.

Sealed First Price Auction Every submits their bidin secret. Highest bidder pays the amount theybid.

Sealed Second Price AuctionAlso called theVickrey Auction (VA). Highest bidders pays thesecond highest bid.

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Does it pay to lie?English Auction

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Does it pay to lie?English Auction No

Dutch Auction

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Does it pay to lie?English Auction No

Dutch Auction Yes

Sealed First Price Auction

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Does it pay to lie?English Auction No

Dutch Auction Yes

Sealed First Price Auction Yes

Sealed Second Price Auction

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Does it pay to lie?English Auction No

Dutch Auction Yes

Sealed First Price Auction Yes

Sealed Second Price AuctionNo

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Does it pay to lie?English Auction No

Dutch Auction Yes

Sealed First Price Auction Yes

Sealed Second Price AuctionNo

What is the major difference between VA and English

Auction?

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Does it pay to lie?English Auction No

Dutch Auction Yes

Sealed First Price Auction Yes

Sealed Second Price AuctionNo

What is the major difference between VA and English

Auction? Privacy of valuation

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Why is Truth-Telling the Dominant Strategy

for VA?

“Proof” :Simple case, there are two bidders with true valuevi

and bidbi, i = {1, 2}.Bidder 1’s expected payoff is

Pr(b1 > b2)[v1 − b2]

That is, the probability of winning times the payoff(the item’s value minus how much they pay for it).If second term is positive you want to maximizeprobability of winning, otherwise you want tominimize it.

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Auctions with Computerized Agents

Privacy is important – for buyer and seller.

Mechanism design is supposed to alleviate theseconcerns.

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Generalized Vickrey AuctionA more general model is proposed where each userhas a utility function for some set of goods.

The Generalized Vickrey Auction or Vickrey-Clark-

Groves Auction is a truth-telling mechanism where it

is in everyone’s best interest to reveal their true utility

function.

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Part II

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Money, money, money...Google – over 98% of revenue from advertising

Yahoo! – over 50%....

Together these companies are worth $125 billion,roughly 6 times that of all US airlines.

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Money, money, money...Google – over 98% of revenue from advertising

Yahoo! – over 50%....

Together these companies are worth $125 billion,roughly 6 times that of all US airlines.

YOWZAH!

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A Brief History of Internet Advertising

1.

2.

3.

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A Brief History of Internet Advertising

1. Early (1994) advertising was sold on a“per-impression basis”.

2.

3.

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A Brief History of Internet Advertising

1. Early (1994) advertising was sold on a“per-impression basis”.

2. Targeted advertising introduced by Overture(1997). Generalized first-price auction:advertisers bid to have their ad show up inrelation to chosen keywords. You pay what youbid. Problem: Its not stable in the one-shot case.

3.

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A Brief History of Internet Advertising

1. Early (1994) advertising was sold on a“per-impression basis”.

2. Targeted advertising introduced by Overture(1997). Generalized first-price auction:advertisers bid to have their ad show up inrelation to chosen keywords. You pay what youbid. Problem: Its not stable in the one-shot case.

3. In 2002 Google introduced AdWords Select: ageneralized second price auction:

unique auction model uses NobelPrize-winning economic theory toeliminate . . . that feeling that you’ve paidtoo much

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Generalized Second Price Auction (GSP)

Everytime a keyword is queried, there areN availableadvertising slots.Let bi andvi be the bid and true per-click value foradvertiseri = 1 . . . K. Let g(j) andb(j) be the id and

bid of thejth highest bidder.Slot j is assigned to userg(j) and they are chargedbj+1 for every click

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Generalized Second Price Auction (GSP)

Everytime a keyword is queried, there areN availableadvertising slots.Let bi andvi be the bid and true per-click value foradvertiseri = 1 . . . K. Let g(j) andb(j) be the id and

bid of thejth highest bidder.Slot j is assigned to userg(j) and they are chargedbj+1 for every click

What is aunit of internet advertising?

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User payoff in GSPLet αj be the expected number of clicks on the ad inslot j.Userg(j)’s total valuation for slotj is αjv

(j). Theypayp(j) = αjb

(j+1) so their total payoff is:

αj(v(j) − b(j+1))

What assumptions are being made?

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GSP vs. VCGGSP does not map exactly toVickrey-Clark-Groves(VCG) Mechanism. In VCG,the payment for slotj is defined inductively:

pV,(j) = (αj − αj+1)b(j+1) + pV,(j+1)

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GSP vs. VCGGSP does not map exactly toVickrey-Clark-Groves(VCG) Mechanism. In VCG,the payment for slotj is defined inductively:

pV,(j) = (αj − αj+1)b(j+1) + pV,(j+1)

• In VCG, truth-telling is the dominant strategy.

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GSP vs. VCGGSP does not map exactly toVickrey-Clark-Groves(VCG) Mechanism. In VCG,the payment for slotj is defined inductively:

pV,(j) = (αj − αj+1)b(j+1) + pV,(j+1)

•• In VCG, truth-telling is the dominant strategy.• In GSP, truth-telling is not the dominant strategy:

• Values are $10, $4,$2.• α1 = 200, α2 = 199, α3 = 0• Bidder 1’s payoff for bidding $10 = $1200.

Payoff for shading bid at $3=$1592.

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GSP vs. VCGGSP does not map exactly toVickrey-Clark-Groves(VCG) Mechanism. In VCG,the payment for slotj is defined inductively:

pV,(j) = (αj − αj+1)b(j+1) + pV,(j+1)

• In VCG, truth-telling is the dominant strategy.• In GSP, truth-telling is not the dominant strategy:

• Values are $10, $4,$2.• α1 = 200, α2 = 199, α3 = 0• Bidder 1’s payoff for bidding $10 = $1200.

Payoff for shading bid at $3=$1592.

Question: why doesn’t Google use VCG?Mechanism Design for Internet Advertisting – p.15/22

Static GSP & Envy-Free Equilibria

Consider scenario where bids can constantly change.Eventually we learn information about other people’svaluation. We ask: what kind of equilibrium isattained?

Definition An equilibrium of the static gameΓimposed by GSP islocally envy-free if a player cannotimprove his payoff by exchanging bids with the playerranked one position above him, i.e.∀i ≤ min{N,K}

we haveαisg(i) − p(i) ≥ αi−1sg(i) − p(i−1).

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Envy-Free Equilibria and Stable Matchings

Map this concept to that ofstable matchings.

Lemma 0.0 A locally envy-free equilibrium ofauction Γ is a stable assignment.

Lemma 0.0 Reverse implication is also true,provided the number of bidders is greater than thenumber of available slots.

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One Equilibrium in Particular

Let b∗i = pV,(j−1)

αj−1wherepV is the payment in the

dominant-strategy equilibrium of VCG andj is theposition of bidderi in that equilibrium.

Theorem 0.0 This strategy is an envy-freeequilibrium of game Γ. In this equilibrium, eachbidder’s position and payment is equal to those in thedominant-strategy equilibrium of the game induced byVCG. In any other locally-envy free equilibrium ofgame Γ, the total revenue of the seller is at least ashigh as in this strategy

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a moment to reflect...Essentially they custom-crafted a strategy so that theresults of GSP matched that of VCG. It is notsurprising that its envy-free.

What I think is more interesting is that it considers the

revenue of the seller. Related to an earlier remark in

the paper and other work on AdSense....

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Generalized English Auction (GEA)

Similar to English Auction except bidders areassigned to slots in the order they drop out of theauction.

A simple strategy: increase bid as long as it profitsyou to do so. Surprisingly this leads to the sameequilibrium we saw before.

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Formal Resultαi is known for alli. Valuations are drawn from acontinuous distributionF (·). The user knows theirown valuation as well asF .

Let p(k, h, si) = si −αk

αk−1(si − bk+1) be the price at

which useri drops out, wherek is the number ofbidders remaining,h = (bk+1, . . . , bK) is the historyof bidders.

Theorem 0.0 The strategy given above results in aperfect Bayesian Equilibrium. In this equilibrium thepositions and payoff are the same as in the dominantstrategy equilibrium of VCG.

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Conclusion

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