Brand Display Ads Performance Display Ads

ADVERSE SELECTION AND

AUCTION DESIGN FOR INTERNET

DISPLAY ADVERTISING

NICK ARNOSTI, MARISSA BECK AND PAUL MILGROM APRIL 2014

1

Performance Display Ads: 13-Apr-2014

3

Advertisement Types

!  Goal: create awareness and

a positive product image !  Advertisers typically pay for

reach and repetition.

!  Number of Impressions: large,

specified by contract

!  Price: specified by contract.

!  Sample Advertisers

!  Ford (auto sales)

!  Disney (movie openings)

!  Mayoral candidate (election)

!  Goal: inspire a measurable

action right now

!  Visit a website, fill a form, buy a product.

!  Number of impressions: small,

depends on realized traffic

!  Price: per impression basis

!  Sample Advertisers

!  Hertz (car rental)

!  Amazon (re-targeting)

!  Quicken mortgage (refinance)

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Risk of Adverse Selection?

!  Often have cookies with private

information

!  Can easily distinguish which

websites are performing well.

!  Can get immediate feedback

about ad performance

!  Can link future performance

statistically to todays ads.

!  No cookies.

!  Cannot easily distinguish which

websites are performing well.

!  Cannot get immediate feedback

about ad performance

!  Cannot link future performance

to today’s ads.

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Performance Advertisers Brand Advertisers

Two Common Systems

! 

“Old

Yahoo!

System”

! 

A random selection of impressions with sufficient volume

is set aside for the traditional advertisers.

! 

Remnant impressions are sold by auction.

! 

The system avoids adverse-selection, but can waste

good matching opportunities.

! 

Pure auction system

! 

Impressions sold separately in second-price auctions.

Cost of Old System: Intuitive Analysis

!  Suppose for this example that

!  bidder values of impressions are independent (no adverse selection)

!  80% of impressions are assigned to brand advertisers

!  20% of impressions are assigned to performance advertisers

!  80-20 rule applies: 80% of the value of advertising is associated with the 20%

most valuable impressions

!  Comparing two feasible systems

!  Random set aside: then performance advertisers get just 20% of the maximum value. !  Second-price auction with reserve: performance advertisers get 80% of the value. !  Performance match value is four times higher for the auction!

!  Hypothesis: Adverse selection is a serious problem!

!  Next question: Is there any generality to this comparison? (Yes!)

Auction Model: General IID Values

!  Suppose bidder values are non-negative iid draws X_i,

i=1,…,N from distribution F with density f on (a,b). Let !  Let W be distributed U(0,1), independently of X.

!  Consider a mechanism in which performance advertiser i wins the impression if X_i=X₍₁₎>h(W,X_-(1)).

!  For a “random set aside,”

!  Let =1–Pr{X₍₁₎>h(W,X_-(1))} be the probability that the brand advertiser wins.

!  Notation: Let Y=max X_-1, Z=h(W,X_-1), so 1 wins if X₁>max(Y,Z).

!  Let g(x)=x-(1-F(x))/f(x) be Myerson’s “virtual value” function.

Random Set Asides Are

Pessimal!

9

! 

Theorem. For an auction with threshold pricing using the

preceding selection rule

!  Expected total value is: (1- )E[X₁|X₁ > max(Y,Z)]

!  Expected seller revenue is: (1- )E[g(X₁)|X₁>max(Y,Z)]

!  Expected bidder surplus is: (1- )E[X₁-g(X₁)|X₁>max(Y,Z)]

! 

Corollary. For any fixed , over the set of mechanisms

studied, the random set aside…

!  Minimizes expected total value

!  Minimizes expected seller revenue if g(v) is non-decreasing

!  Minimizes expected bidder surplus if v-g(v) is non-decreasing

Modern

Yahoo!

System

!  All impressions allocated by auction, using proxy bidders.

!  Ghosh, Arpita, Preston McAfee, Kishore Papineni and Sergei Vassilvitskii (2009), “Bidding

for Representative Allocations for Display Advertising.” Journal of Economic Design.

!  For each category of impressions, a proxy bidder bids randomly according to a distribution F chosen to

!  Minimize the “distance” between the distributions of awarded bids and highest opposing

bids.

!  Subject to an average price constraint and to a target number of impressions delivered.

!  Gored by the horns of a dilemma! When a randomized bid comes out…

!  Very High: it always wins, so matching value is not improved for these impressions

!  Very Low: it always loses, so matching is not improved for these impressions

!  Any Other: the assignment depends on the performance bids, so for these impressions,

matching value is improved, but the brand advertiser is vulnerable to adverse selection.

A two-factor model

Adverse Selection vs Matching

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Two-Factor Model

! 

The value of an impression to advertiser

n

is

x

=

cm

!  where c is the (random) common value factor and

!  N≥2 is the (random) number of bidders

!  m_n is the (random) match value factor for bidder n

!  m=(m₁,…,m_N).

! 

Key Assumption

: The common value factor

c

is statistically

independent of the match value factor vector (

N,m

).

! 

Definition

. A mechanism for assigning impressions to

advertisers is

adverse selection free

if the event that the

mechanism chooses to show the brand ad is statistically

Direct Mechanisms

! 

Each performance advertiser j reports its value x

.

! 

A direct mechanism is a pair (z,p). When N=n,

! 

The impression is assigned to the brand advertiser with

probability

z

(

x

,…,

x

).

! 

The impression is assigned to performance advertiser

j

with

probability

z

(

x

,…,

x

).

! 

The expected payment by performance advertiser

j

is

p

(

x

,…,

x

).

Desirable Properties

! 

Definitions. An display ad allocation mechanism is:

! An auction if only winning bidders make payments

! Strategy-proof if truthful bidding is always optimal for

performance bidders.

! Deterministic if its allocation/payment rules are not randomized

! Anonymous if it symmetric among performance bidders

! Adverse-selection free if z₀ and c are statistically independent for

all joint distributions of (N,m) and all distributions of c.

! False-name proof if adding another bid below the lowest current

bid never affects the winner or price.

Main Theoretical Result

! 

Theorem. The set of all high-achieving direct

mechanisms form a one-parameter (

≥

1) family,

which we call the modified second-bid (MSB) auctions.

! 

For parameter , the highest performance bidder wins if its

bid

b

≥

b

, where

b

and

b

are the first- and

second-highest performance bids.

! 

If the performance bidder wins, its price is

b

.

! 

If the brand bidder wins, its price is as determined by its

contract.

! 

If the bid distributions are non-atomic, there is exactly one

auction in this family that sells a fraction of impressions to

brand advertisers.

The Familiar Properties

!  Lemma. A auction is deterministic, anonymous and strategy-proof if and

only if it is a threshold auction, which means that

!  j’s bid b_j wins if and only if it is highest and exceeds a threshold h(b_-j), and !  in the event that j wins, she pays h(b_-j).

Adverse Selection Free

!  Lemma. A mechanism is adverse-selection free if and only if z₀(.) is

homogeneous of degree zero.

!  Proof. If z₀(.) is homogeneous of degree zero, then z₀(x)=z₀(cm)=z₀(m),

which is statistically independent of c because c and m are independent.

!  If z₀(.) is NOT homogeneous of degree zero, find a vector m and two

common values c and c’ such that z₀(cm)>z₀(c’m). Specify distributions such that m is the only possible value for the random match values and the two common values each have probability 0.5. Then, the correlation of c and z₀

is ±1: the two random variables are not independent.

!  In terms of the previous lemma, this means that such a mechanism is

adverse-selection free if and only if h(._{) is homogeneous of degree one.}

Example

! 

Consider the mechanism in which the highest performance

bidder wins if its bids is at least times the mean of the lower

performance bids.

! 

This mechanism is…

!  Adverse-selection free, because z₀ is homogeneous of degree zero, but

!  Not false-name proof, because a performance bidder’s chance of winning is increased by submitting additional bids that are very low using a “false name.”

False-Name Proof

!  Lemma. A mechanism is false-name proof if and only if it depends only on

the two highest performance bids b₍₁₎ and b₍₂₎.

!  Proof. By induction on the number of bids…

!  Adding this restriction to the previous one means that h(b_(-1))=h(b₍₂₎)= b₍₂₎.

Computations

Base Case: Power Law Distribution

Power Law Distribution

! 

Assume that the variables m

are drawn IID from a

power law distribution: Pr{m

>

µ

}=

µ

_.

! 

Notation:

! 

m

=

k

order statistic

r

=

m

/

m

! 

Four implications of the power law distribution.

1. 

ln

(

m

) has an exponential distribution with mean 1/

a.

2. 

r

and

m

are statistically independent

3. 

r

has the power law distribution with parameter

a

.

4. 

E

[

r|r>

α

]

=

α

E

[

r

]

Computing

α

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! 

Proposition. Assume that match values are IID

draws from a power law distribution with

parameter

a.

Then

,

the unique high-achieving

mechanism that sells a fraction 1-

λ

to

Power Law Performance Gains

! 

Setting

α

>1, the welfare and payoff measures in MSB

auctions

all increase by a factor

of

α

compared to the

random set aside.

! 

For easy arithmetic, let

c

=1.

! Expected value from performance impressions:

! Expected revenue from performance impressions:

! Expected bidder profit from performance impression:

ERP =E[αm(2)₁

{r>α}]=αE[m

(2)_{]Pr{r >α}=α(1−λ)E[m}(2)_]

EVP =E[m(1)₁

{r>α}]=E[m (2)_r1

{r>α}]=E[m

(2)_{]E[r|r >α]Pr{r >α}}

=E[m(2)_{]αE[r](1−λ)=α(1−λ)E[m}(1)_]

EPP=EVP−ERP =α(1−λ)E[m(1)−m(2)]

Power Law Gains Can be

Very

Large

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! 

Consider the 80-20 rule, according to which 80% of the

value of performance ads come from 20% of impressions.

! E[r1_{{r in its top quintile}} ] = .8xE[r].

! 

Sample calculations using power law a=1.16.

! 

Case 1: 80% of ads reserved for brand: =0.8.

" Changes expected value from 20%xE[c]E[m₍₂₎]E[r] to 80%xsame. " So, =4.0. Hence, the performance ad revenues and profits both

increase by 300%.

! 

Case 2: 50% of ads reserved for brand: =0.5.

" This leads to =1.8 and the performance ad revenues and profits

Worst-Case Performance

! 

The approach we have taken is axiomatic, so no optimality

properties are proved.

!  How much is lost?

!  If there is no actual adverse selection and we could run a second price auction, what is the maximum percentage loss of value as we vary the number of bidders, the parameter a of the power law, and the fraction

λ of impressions for brand advertisers?

! 

Theorem. The worst-case value loss from the MSB auction is less

than 6% of the first-best value.

Omitting False-Name Proofness

! 

Theorem. If the match values are IID draws from a

power law distribution, then there exists some

such that the mechanism that maximizes total

expected value among otherwise high-achieving

mechanisms that may fail to be false-name proof

uses the following assignment rule, which depends

on the ratio of the highest to the LOWEST

performance bid:

β

>

1

z

(

x

,

…

,

x

)

=

1

x(1)_=x( 2)

Other Distributions

! 

Conjecture: Results similar to the power law findings

also hold for other “fat-tailed” distributions, for

which the hazard rate of the distribution of ln(

m

) is

non-increasing.

Preliminary

Data Summary

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Label

Lambda

(nearest .50) Alpha

% Revenue Change

% Profits Change

Pull 1 .51 50.0 13.16 2.55

Pull 552 .52 3.0 48.62 28.93

Pull 2151 .58 4.0 61.31 29.70

Pull 2445 .48 12.0 20.52 26.06

Pull 5757 .47 2.0 34.66 64.21

Pull 9638 .75 1.7 10.75 195.67

Pull 18050 .52 4.0 30.38 11.36

Pull 18316 .50 20.0 -11.16 -27.36

Pull 18316b .51 20.0 -14.57 -36.69

Pull 18536b .50 6.0 75.13 24.48

Pull 8864b .48 3.0 18.03 4.64