Google’s Auction for TV ads. Noam Nisan Tel-Aviv and Hebrew University Joint work with: Jason Bayer, Deepak Chandra, Tal Franji, Robert Gardner, Yossi Matias, Neil Rhodes, Misha Seltzer, Danny Tom, Hal Varian, Dan Zigmond . sells TV ads.
Tel-Aviv and Hebrew University
Joint work with: Jason Bayer, Deepak Chandra, Tal Franji, Robert Gardner, Yossi Matias, Neil Rhodes, Misha Seltzer, Danny Tom, Hal Varian, Dan Zigmond
Why buy from Google?
Workflow for advertisers:
The auction runs, your ad is scheduled and aired, you get a detailed report, and you pay Google (and then Google pays publishers.)
Publishers receive & air ad schedule
Publishers Daily Inventory
Auction runs daily
Google bills advertisers
Advertisers Bid DB
m slots for sale; slot j has reserve price rj ≥ 0
n bidders. Bidder i has:
Budget limit bi
Value vij for each slot j
Set of slots Si won by each bidder i.
Price pj for each slot j
rj ≤ pj ≤ vij (for j in Si)
∑ j in Sipj ≤ bi
Efficiency (total value)
Incentive CompatibilityBasic Model
Optimize Revenue: Maximize ∑jpj ?
Optimize Social Welfare: Maximize ∑ j in Sivij ?
Solution: D(p)=100 when p=$2
Definition:S is the demand of i at prices p1…pm if it is within budget (∑ j in Spj ≤ bi) and it maximizes utility. I.e. for every T within budget we have that ∑ j in T (vij-pj)≤ ∑ j in S (vij-pj).
Definition:S1…Sn and p1…pm are at an equilibrium if:
If slots were infinitely divisible then:
Input:p1…pm ; vi1…vim ; b
Output: S within budget (∑ j in Spj ≤ bi) that maximizes ∑ j in S (vij-pj)
Complexity: Knapsack NP-hard
Optimal Fractional solution:
Why not FPTAS?
at most mvmax/δ rounds
BUG: slots may be left un-allocated….
Definition: “Gross Substitutes” = it doesn’t happen
Theorem: If “Gross Substitutes” then (δ-) Walrasian equilibrium [Kelso and Crawford]
Example: Homogenous slots
Example: “Unit demand” – demand is never more than a single unit [Demange, Gale, and Sotomayer]
An algorithm for maximum-weight bipartite matching
Reality is not “Gross substitutes”
What to do with these?
Our Solution: remnant-sale round