Internet Economicsכלכלת האינטרנט

Class 8 – Online Advertising (part 2)

1

Sponsored search auctions

2

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

Sponsored search auctions

3

Search keywords keywordskeywordsAd slots

Bidding

4

• A basic campaign for an advertiser includes:

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

Click Through Rates

5

• Are all ads equal?

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

• Need to understand user behavior.

Click Through rate

6

9%4%

2%

0.5%

0.2%

0.08%

Click Through rate

7

c1

c2

c3

c4

…

…

ck

Formal model

8

• 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

9

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*0.8 + 8*0.03 + 2*0.01

GSP

10

• 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

11

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

12

• 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)

VCG prices

13

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

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

14

Reminder

15

• In an earlier 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

16

Simultaneous Ascending Auction (sketch)

1. Start with zero prices.

2. Each bidder reports his favorite item

3. Price of over-demanded items is raised by $1.

4. Stop when there are no over-demanded items.– Bidders win their demands at the final prices.

17

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

Market clearing prices

18

• Conclusion: In a multi-unit auction with unit-demand bidders market-clearing prices exist.

• And we saw that:– Such equilibrium exists.– these market clearing prices are exactly the VCG prices– the allocation is efficient

“market-clearing prices”:• every bidder receives his favorite item (given the prices)• all items are allocated (unless their price is 0).

Market clearing prices

19

p1 p2 p3 p4 p5

“Envy-free” result: I don’t want Tinky-Winky’s item for the price that he pays.

“market-clearing prices”:• every bidder receives his favorite item (given the prices)• all items are allocated (unless their price is 0).

Market clearing prices

20

• And we saw that:– Market-clearing prices exist.– Easy to find:

• Ascending-price auctions• VCG prices!!!

– the allocation is always efficient

• Again, an easy way to find market clearing prices: calculate VCG prices.

Sponsored search as multi-unit auction

21

• 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.– No advertiser “envies” another advertiser and wants to

have their slot+price.

Slot 1Slot 2p2=3

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

Market Clearing Prices

22

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

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

23

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).

Equilibrium

24

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).

That is, each player bids the VCG price of the winner above them.

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

Equilibrium bidding

25

b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

b4=1The 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?

p1= $5.625

p2=$1.67

p3= $1

The VCG prices

Step 1

26

• 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:

Under the market clearing prices: t will not want to get slot j and pay pj.

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

≥

Proof (cont.)

27

Left to show:bidding as we proposed is a Nash equilibrium: – no bidder will benefit from deviating given the other bids.

Claim: a Nash equilibrium is when each player i bids price pi-1 (bidder 1 can bid any number > p1).

Step 2: equilibrium

28

• Under GSP, i wins slot i and pays pi (=bi+1).

• 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=pi-1 , bi+1=pi , bi+2=pi+1

bi

bi+1

bi+2

Equilibrium bidding

29

b1=10

b2=8

b3=2

c1=0.08

c2=0.03

c3=0.01

Slot 1

Slot 2

Slot 3

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

p1= $5.625

p2=$1.67

p3= $1

Step 2: equilibrium

30

• 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-2=pi-3 , bi-1=pi-2 , bi=pi-1

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.

• GSP is efficient in equilibrium!

• Many assumptions: no budgets, no brand advertisers, single-keyword market, clicks are all the same,…

31

Online advertising - 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…

32

Now let’s play…

33

1. Party time

34

Balloons in the bag game

35

• There are three balloons in the bag.– Either two blue and one red (“blue bag”)– Or one blue and two red (“red bag”)– There is a 50% chance of either majority

• Each student in his turn will:– Take a balloon out of the bag, observe its color without

telling the class.– Put ball back in bag.– After observing the ball, the student will guess whether

the bag has blue/red majority.

• How many students were right?

Analysis

36

• The first student:– If observed blue, then “most chances” that we have blue majority,

therefore a rational student will guess what he saw.• The second student:

– Knows that the first student guessed what he saw.– Therefore, actually observes two draws from the bag.– If he also sees blue, say blue. If red, indifferent (let’s say he reports

what he saw).• Third student:

– Knows that the two previous students guessed what they observed.– If the first two students said blue, will also guess blue (even if he

sees Red).• Fourth student:

– If the first two guessed blue, the third does not tell anything.– will also guess blue (even if he sees Red).

Analysis

37

• If the first two students said blue, the rational thing for every student to guess is blue.

• With a red bag, 1/9 chance that the two first students will guess “blue”

– And they are doing the right thing.

Meaning

38

• The sequential nature of the game leads to scenarios where players ignore their private knowledge

• Information is not aggregated

• An inefficient outcome my be chosen.

• “information cascade in social networks” – next class.

Examples

39

• Choosing a restaurant

• Looking at the sky

• Fashion, going to a movie, voting

40

2. Guess the average

Guess-the-average game

41

• 10 students will receive notes with numbers– Keep secret from other students.

• Goal: guess the average of the 10 numbers.

• Each student with a note will write a guess on a note.

• The closest bid to the average wins.