[PPT] - ADVERSE SELECTION AND AUCTION DESIGN FOR INTERNET DISPLAY PowerPoint Presentation

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ADVERSE SELECTION AND AUCTION DESIGN FOR INTERNET DISPLAY ADVERTISING

NICK ARNOSTI, MARISSA BECK AND PAUL MILGROM DECEMBER 2015

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“Half the money I spend on advertising is wasted; the trouble is, I don’t know which half.”

John Wanamaker, Advertising pioneer

Old Advertisers & New

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Old-Fashioned “Brand” Ads

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New-Fashioned “Performance” Ads

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Display Advertisement Types

¨ Goal: reach & repetition

¤ For awareness and image

¨ Common Characteristics

¤ Targeted to a large group ¤ Large number of Impressions ¤ Guaranteed delivery

¨ Sample Advertisers

¤ Ford (weekend auto sale) ¤ Disney (movie openings) ¤ Shopping Center (location)

¨ Goal: measurable action now

¤ Click, fill form, or buy.

¨ Common Characteristics

¤ Targeted to an individual ¤ Smaller number of impressions ¤ Sell individual impressions

¨ Sample Advertisers

¤ Amazon (re-targeting) ¤ Hertz (car rental) ¤ Quicken mortgage (refinance)

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Brand Ads Performance Ads

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Danger of Adverse Selection

¨ Mostly buy large numbers of

impressions.

¨ Receive deferred, aggregated

data about performance of the whole ad campaign

¨ Cannot easily distinguish low-

performing ads and publishers

¨ Mostly select individual

impressions using private cookies.

¨ Receive immediate, detailed

data about the performance of individual ads

¨ Can quickly identify low-

performing ads and publishers

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Brand Advertisers Performance Advertisers

If brand and performance advertisers’ values are “positively correlated,” then brand advertisers may suffer adverse selection.

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Modeling the problem

Matching with Adverse Selection

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Model

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¨ There are 𝑂 + 1 advertisers, with 𝑂 ≥ 2 ¨ The value of an impression to advertiser i is 𝑌' = 𝐷𝑁'

¨ 𝐷 is the (random) common value factor and

¤ 𝑁' is the (random) match value factor for bidder i ¨ Key Assumptions

1.

Advertiser 0 (the “brand advertiser’) does not observe 𝑌+

2.

Performance advertisers 𝑜 = 1,… ,𝑂 observe their values 𝑌/ Define 𝑌 = 𝑌0,… ,𝑌/ .

3.

The common value factor 𝐷 is statistically independent of the random vector 𝑁 ≝ (𝑁+,… ,𝑁4)

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A Market Design Approach

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¨ Compare the “restricted-worst-case efficiency” (and

later, revenues) of alternative mechanisms.

¨ The mechanisms considered are:

1.

“Bayes optimal” mechanism

2.

Our benchmark: “Omniscient” mechanism with C observed

3.

Second-price auction

4.

Our new “Modified second-bid auction” in which the highest performance bidder wins if the ratio of the highest to second-highest performance bid exceeds a threshold.

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OPT …and its drawbacks

Bayesian Optimal Mechanism

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Optimal Mechanism Formulation

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¨ 𝑨'(𝑌) is probability that 𝑗 wins, given 𝑌 ¨ 𝑞'(𝑌) is 𝑗’s expected payment, given 𝑌 ¨ Efficiency Objective

¤ Goal is to maximize 𝐹 ∑

𝑌'𝑨'(𝑌)

/ ';+

n subject to dominant-strategy incentive constraints and

participation constraints

¤ Let OPT be the mechanism that does that.

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Example

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¨ Assume that 𝑁

0,… ,𝑁/ are IID and that…

𝑄 𝐷 = 1 = 𝑄 𝐷 = 2 = 0

=

𝐺𝑝𝑠 𝑘 = 1,2,3, 𝑄 𝑁

D = 1 = 𝑄 𝑁 D = 2 = 𝑄 𝑁 D = 4 = 0 F

3 < 𝐹 𝑁+ < 4

¨ So, it is efficient to assign this impression to a performance

advertiser 𝑘 ≠ 0 only if and only if 𝑁

D = 4.

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OPT in the Example

12 ¨ The expected-efficiency-maximizing assignment with 𝑂 = 2 is:

¤ There are two easy conditions to analyze:

n If 𝑌(0) ∈ {1,2}, then 𝑁(0) ≤ 2 < 𝐹[𝑁+] ⇒ brand advertiser wins n If 𝑌(0) = 8, then 𝑁(0) = 4 > 𝐹[𝑁+] ⇒ top performance advertiser wins

¤ If 𝑌(0) = 4, assignment hinges on 𝑌(=) and particularly whether

𝐹[𝑁 0 |𝑌(0), 𝑌(=)] ≷ 𝐹[𝑁+].

n If 𝑌(=) = 1, then 𝑁(0) = 4 ⇒ top performance advertiser wins n If 𝑌(=) = 2 or 4, then E M(0) 𝑌 0 ,𝑌 =

= 3 < 𝐹[𝑁+] ⇒ brand advertiser wins

n If 𝑌(=) = 2, then Pr 𝐷 = 1, 𝑁 0 = 4, 𝑁 = = 2 𝑌 0 ,𝑌 =

= Pr 𝐷 = 2, 𝑁 0 = 2,𝑁 = = 1 𝑌 0 ,𝑌 = = X

Y.

n If 𝑌(=) = 4, then Pr 𝐷 = 1, 𝑁 0 = 𝑁 = = 4 𝑌 0 ,𝑌 =

= Pr{𝐷 = 2, 𝑁 0 = 𝑁 = = 2|𝑌(0),𝑌(=)} = X

Y.

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Three Concerns about OPT

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¨ The example highlights some troublesome attributes of OPT

1.

Sensitivity: OPT is sensitive to detailed distributional assumptions.

2.

False-name bidding: Performance advertiser 𝑜 with value 𝑌/ = 4 can benefit by submitting a additional, false-name bid of 𝑌/

Z = 1

(because that encourages the auctioneer to infer that 𝑁/ = 4 whenever 𝑌/ is the maximum performance value.)

3.

Adverse selection: The brand advertiser wins 4/9 of high-value impressions, but 7/9 of low-value ones.

n

This possibility can be problematic, especially if the brand advertiser is uninformed about the other bidders and the model parameters, and so is challenged even to estimate these fractions.

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OMN, in which the auctioneer observes both the bids and C

The Omniscient Benchmark

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OMN Benchmark

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¨ Extreme assumption: the auctioneer can gather

perfect information about the common factor C and can allocate without facing incentive constraints.

¨ Auctioneer could then achieve this value:

𝑊 𝑃𝑁𝑂 = 𝐹 max 𝑌+, 𝑌0, … , 𝑌/ ,

𝑥ℎ𝑓𝑠𝑓 𝑌+ = 𝐷𝐹[𝑁+]

¨ Performance of last two mechanisms is measured

relative to 𝑊 𝑃𝑁𝑂 .

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Modified Second Bid auction characterized by its properties

MSB Characterization

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Some Mechanism Properties

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¨ A mechanism is

¤ anonymous (among performance advertisers) if... ¤ strategy-proof if… ¤ fully strategy-proof if, in addition, it is both

n bidder false-name proof: no bidder can benefit by submitting

multiple bids, and

n publisher false-name proof: the seller cannot benefit by

submitting “low” bids (below all performance bids)

¤ adverse-selection free if for every joint distribution on

(𝐷, 𝑁) such that 𝐷 and 𝑁 are independent, 𝑨+ 𝑌 is statistically independent of 𝐷.

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Characterization Theorem

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¨ Definition. A direct mechanism is a modified second bid auction

if for some 𝛽 ≥ 1,

¤ If

d X d Y > 𝛽, then the highest performance advertiser wins & pays 𝛽𝑌 = .

¤ If

d X d Y ≤ 𝛽, then the brand advertiser wins (and pays its contract price).

¨ Theorem. A deterministic mechanism (𝑨,𝑞) is anonymous, fully

strategy-proof, and adverse selection free if and only if it is a modified second bid auction.

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Proof Ideas

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1.

Deterministic & strategy-proof mechanism ⇔ threshold auction.

2.

…+Anonymous ⇔ the same threshold function for all performance bidders.

3.

…+False-name proof ⇔ the threshold depends

nly on the second highest bid.

4.

…+Adverse-selection free ⇔ the allocation depends on ratio of two highest bids.

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MSBα : modified second-bid auction SPr : second-price auction with reserve

Comparing MSBα and SPrto OMN

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Assumptions for Comparison

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¨ Evaluate MSBα and SPr mechanisms in worst case over

a limited family of environments, in which…

¤ 𝑁

0, … ,𝑁4 are IID from a distribution 𝐺.

¤ 𝐷 is drawn from distribution 𝐻. ¤ 𝑂 ≥ 2 and 𝐹 𝑁+ ≥ 0 are free to vary.

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Efficiency Performance

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¨

Theorem. (Comparing 𝑇𝑄

h and 𝑁𝑇𝐶j to 𝑃𝑁𝑂)

1.

Assuming Nash equilibrium bidding by the brand advertiser, both MSB and SP have similar worst case performance: inf

n,o,4p=,q[rs]p+max j

𝑊 𝑁𝑇𝐶j 𝑊(𝑃𝑁𝑂) = 1 2 inf

n,o,4p=,q[rs]p+max h

𝑊 𝑇𝑄

h

𝑊(𝑃𝑁𝑂) = 1 2

2.

Further restricting 𝐺 and/or 𝐻 to be drawn from power law distributions 𝒬, inf

n∈𝒬,o∈𝒬,4p=,q[rs]p+max h