0 ADVERSE SELECTION AND AUCTION DESIGN FOR INTERNET DISPLAY ADVERTISING NICK ARNOSTI, MARISSA BECK AND PAUL MILGROM DECEMBER 2015
Old Advertisers & New 1 “Half the money I spend on advertising is wasted; the trouble is, I don’t know which half.” - John Wanamaker, Advertising pioneer
Old-Fashioned “Brand” Ads 2
New-Fashioned “Performance” Ads 3
Display Advertisement Types 4 Brand Ads Performance Ads ¨ Goal: reach & repetition ¨ Goal: measurable action now ¤ For awareness and image ¤ Click, fill form, or buy. ¨ Common Characteristics ¨ Common Characteristics ¤ Targeted to a large group ¤ Targeted to an individual ¤ Large number of Impressions ¤ Smaller number of impressions ¤ Guaranteed delivery ¤ Sell individual impressions ¨ Sample Advertisers ¨ Sample Advertisers ¤ Ford (weekend auto sale) ¤ Amazon (re-targeting) ¤ Disney (movie openings) ¤ Hertz (car rental) ¤ Shopping Center (location) ¤ Quicken mortgage (refinance)
Danger of Adverse Selection 5 Brand Advertisers Performance Advertisers ¨ Mostly buy large numbers of ¨ Mostly select individual impressions. impressions using private cookies. ¨ Receive deferred, aggregated ¨ Receive immediate, detailed data about performance of the data about the performance of whole ad campaign individual ads ¨ Cannot easily distinguish low- ¨ Can quickly identify low- performing ads and publishers performing ads and publishers If brand and performance advertisers’ values are “positively correlated,” then brand advertisers may suffer adverse selection.
Matching with Adverse Selection 6 Modeling the problem
Model 7 ¨ 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 Advertiser 0 (the “brand advertiser’) does not observe 𝑌 + 1. Performance advertisers 𝑜 = 1,… ,𝑂 observe their values 𝑌 / 2. Define 𝑌 = 𝑌 0 ,… ,𝑌 / . The common value factor 𝐷 is statistically independent of the 3. random vector 𝑁 ≝ (𝑁 + ,… ,𝑁 4 )
A Market Design Approach 8 ¨ Compare the “restricted-worst-case efficiency” (and later, revenues) of alternative mechanisms. ¨ The mechanisms considered are: “Bayes optimal” mechanism 1. Our benchmark: “Omniscient” mechanism with C observed 2. Second-price auction 3. Our new “Modified second-bid auction” 4. in which the highest performance bidder wins if the ratio of the highest to second-highest performance bid exceeds a threshold.
Bayesian Optimal Mechanism 9 OPT …and its drawbacks
Optimal Mechanism Formulation 10 ¨ 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.
Example 11 ¨ Assume that 𝑁 0 ,… ,𝑁 / are IID and that… 𝑄 𝐷 = 1 = 𝑄 𝐷 = 2 = 0 = D = 4 = 0 𝐺𝑝𝑠 𝑘 = 1,2,3, 𝑄 𝑁 D = 1 = 𝑄 𝑁 D = 2 = 𝑄 𝑁 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 .
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 .
Three Concerns about OPT 13 ¨ The example highlights some troublesome attributes of OPT Sensitivity: OPT is sensitive to detailed distributional assumptions. 1. False-name bidding : Performance advertiser 𝑜 with value 𝑌 / = 4 2. 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.) Adverse selection : The brand advertiser wins 4/9 of high-value 3. impressions, but 7/9 of low-value ones. This possibility can be problematic, especially if the brand advertiser is n uninformed about the other bidders and the model parameters, and so is challenged even to estimate these fractions.
The Omniscient Benchmark 14 OMN, in which the auctioneer observes both the bids and C
OMN Benchmark 15 ¨ 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 + , 𝑌 0 , … , 𝑌 / , 𝑥ℎ𝑓𝑠𝑓 𝑌 + = 𝐷𝐹[𝑁 + ] ¨ Performance of last two mechanisms is measured relative to 𝑊 𝑃𝑁𝑂 .
MSB Characterization 16 Modified Second Bid auction characterized by its properties
Some Mechanism Properties 17 ¨ 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 .
Characterization Theorem 18 ¨ Definition . A direct mechanism is a modified second bid auction if for some 𝛽 ≥ 1 , 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). ¤ If ¨ 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.
Proof Ideas 19 Deterministic & strategy-proof mechanism ⇔ 1. threshold auction. …+Anonymous ⇔ the same threshold function for 2. all performance bidders. …+False-name proof ⇔ the threshold depends 3. only on the second highest bid. …+Adverse-selection free ⇔ the allocation 4. depends on ratio of two highest bids.
Comparing MSB α and SP r to OMN 20 MSB α : modified second-bid auction SP r : second-price auction with reserve
Assumptions for Comparison 21 ¨ Evaluate MSB α and SP r mechanisms in worst case over a limited family of environments, in which… ¤ 𝑁 0 , … ,𝑁 4 are IID from a distribution 𝐺 . ¤ 𝐷 is drawn from distribution 𝐻 . ¤ 𝑂 ≥ 2 and 𝐹 𝑁 + ≥ 0 are free to vary.
Efficiency Performance 22 Theorem . (Comparing 𝑇𝑄 h and 𝑁𝑇𝐶 j to 𝑃𝑁𝑂 ) ¨ Assuming Nash equilibrium bidding by the brand advertiser, both MSB and SP 1. have similar worst case performance: 𝑊 𝑁𝑇𝐶 j 𝑊(𝑃𝑁𝑂) = 1 n,o,4p=,q[r s ]p+ max inf 2 j 𝑊(𝑃𝑁𝑂) = 1 𝑊 𝑇𝑄 h n,o,4p=,q[r s ]p+ max inf 2 h Further restricting 𝐺 and/or 𝐻 to be drawn from power law distributions 𝒬 , 2. 𝑊(𝑃𝑁𝑂) = 1 𝑊 𝑇𝑄 h n∈𝒬,o∈𝒬,4p=,q[r s ]p+ max inf 2 h 𝑊 𝑁𝑇𝐶 j n∈𝒬,o,4p=,q[r s ]p+ max inf 𝑊(𝑃𝑁𝑂) ≈ 0.948 j
Revenue Performance 23 ¨ Theorem . Fix a number of bidders N and assume that the publisher shares in the rents from brand advertising in any fixed proportions, say (𝜀,1 − 𝜀) . ¨ If 𝐺 is a power law distribution, then there is some 𝛽 such that 𝑁𝑇𝐶 j achieves at least 94.8% of the expected revenue from the corresponding expected-revenue-maximizing strategy- proof auction 𝑆𝐹𝑊𝑁𝐵𝑌 .
Conclusion 24 ¨ Adverse selection can be neutralized, without encouraging false-name bidding, provided that 𝑌 / = 𝐷𝑁 / and 𝐷 and 𝑁 are independent. ¨ The cost of doing that is low, even without observing the common value factor 𝐷 , provided that the tails of the distribution are fat (power law). ¨ For real applications, we need to evaluate… ¤ Is adverse selection important? ¤ Are match values independent? ¤ Are match-value distributions fat-tailed?
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