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On Revenue in the Generalized Second Price Auction Brendan Renato - - PowerPoint PPT Presentation
On Revenue in the Generalized Second Price Auction Brendan Renato - - PowerPoint PPT Presentation
On Revenue in the Generalized Second Price Auction Brendan Renato va Lucier Paes Leme Tardos (MSR-NE) (Cornell) (Cornell) Sponsored Search Auctions Sponsored Search Auctions Two AdAuctions Mechanisms Generalized Second
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Sponsored Search Auctions
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Generalized Second Price Auction Vickrey-Clarke-Groves Mechanism
Two AdAuctions Mechanisms
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GSP VCG Two AdAuctions Mechanisms
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GSP VCG
Main Question: How do those mechanisms compare from a game-theoretic viewpoint ?
Two AdAuctions Mechanisms
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GSP VCG Two AdAuctions Mechanisms
- sort by bid
- sort by bid
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GSP VCG Two AdAuctions Mechanisms
- sort by bid
- pricing = next
highest bid
- sort by bid
- complicated
pricing rule
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GSP VCG Two AdAuctions Mechanisms
- Simple
- Industrial
standard
- Complicated
- Optimal in
theory
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With respect to which metric ?
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With respect to which metric ?
Users Advertisers Search Engine
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With respect to which metric ?
Users
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads
Advertisers Search Engine
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With respect to which metric ?
Users
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads
Revenue
Advertisers Search Engine
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With respect to which metric ?
Users
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads
Revenue (our focus)
Advertisers Search Engine
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With respect to which metric ?
Advertisers Users Search Engine
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads
Social Welfare = ∑ Clicks . (value/click)
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With respect to which metric ?
Users
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads
?
Advertisers Search Engine
Social Welfare = ∑ Clicks . (value/click)
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With respect to which metric ?
Users
Clicks * (value/click – pay/click) Clicks * pay/click Usefulness of ads [Varian], [Eldeman, Ostrovsky, Schwarz], [Paes Leme, Tardos], [Lucier, Paes Leme], [Caragiannis, Kaklamanis, Kanellopoulos, Kyropoulou], [CKKKLPLT], [Athey, Nekipelov], [Ellison, Athey], …
Advertisers Search Engine
Social Welfare = ∑ Clicks . (value/click)
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Warm-up: When we have one ad slot…
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Which ad to place and how much to charge?
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Which ad to place and how much to charge?
$0.03 / click $0.02 / click $0.01 / click
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Which ad to place and how much to charge?
$0.03 / click $0.02 / click $0.01 / click
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Which ad to place and how much to charge?
$0.03 / click $0.02 / click $0.01 / click
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Which ad to place and how much to charge?
Pays $0.02 / click (second highest bid)
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Selling Display Ads
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Selling Display Ads
Single ad slot Second-price auction
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Selling Display Ads
Single ad slot Second-price auction
- simple
- easy to bid (truthful)
- maximizes welfare
- maximizes revenue with
- ptimal reserve r
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Selling Display Ads
Single ad slot Second-price auction
Theorem (Myerson’81) The revenue-optimal auction* for a single item is the second price auctions with a reserve price. * under suitable assumptions
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Usually we have many ad slots …
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… and not all of them are equal
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… and not all of them are equal
Position Auctions auctioning positions on webpages How to place ads and how to charge for them with multiple positions.
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1) Without uncertainty: GSP revenue is at least ½ of a natural VCG-like benchmark 2) With uncertainty (Bayesian setting): GSP with appropriate reserve price extracts constant fraction of the optimal revenue 3) Revenue and Welfare: What are the trade-offs?
Our Results
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Our Results
1) Without uncertainty: GSP revenue is at least ½ of a natural VCG-like benchmark 2) With uncertainty (Bayesian setting): GSP with appropriate reserve price extracts constant fraction of the optimal revenue 3) Revenue and Welfare: What are the trade-offs?
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Related Work
Position Auctions model due to [Edelman, Ostrovsky, Schwarz] and [Varian], who study revenue of GSP for a particular class
- f equilibria.
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Related Work
Position Auctions model due to [Edelman, Ostrovsky, Schwarz] and [Varian], who study revenue of GSP for a particular class
- f equilibria.
In contrast, we study revenue of GSP over all equilibria in settings with uncertainty.
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- n advertisers and n slots
- slot i has click through rate
- values per click i.i.d.
- distributions are nice*
- reserve price r
Position Auctions Model
* nice = regular, i.e., revenue curve is concave, e.g., uniform, exponential, normal, …
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- Strategy for i : a bidding function
- Assume non-overbidding
- Bidding functions form a Bayes-Nash
equilibrium, i.e., no player benefits from changing bids even after learning their valuation
Position Auctions Model
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α1 α2 α3
Position Auctions Model
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α1 α2 α3
b1(v1) b2(v2) b3(v3)
Position Auctions Model
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α1 α2 α3
b1(v1) b2(v2) b3(v3)
Position Auctions Model
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α1 α2 α3
b1(v1) b2(v2) b3(v3)
- Remove bids below r
- Sort by bid
- Charge next highest bid or r [GSP]
- Charge a complicated function [VCG]
Position Auctions Model
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Thm: If are iid according to a regular distribution, then GSP with the appropriate reserve price r extracts at least a 1/6 fraction of the revenue of the
- ptimal mechanism.
Our Main Result
is a Bayes-Nash equilibrium of GSPr then its revenue is at least 1/6 of the revenue of any mechanism and any equilibrium of this mechanism.
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Thm: If are iid according to a regular distribution, then GSP with the appropriate reserve price r extracts at least a 1/6 fraction of the revenue of the
- ptimal mechanism.
Our Main Result
Why is this good ? 1/6 is an absolute worst-case theoretical guarantee. It assumes very little about distributions. The guarantee doesn’t depend on # of players, alphas,
- r characteristics of the distribution (besides regularity).
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Our Main Result
Application: We give guidelines for setting reserve prices in GSP. Myerson’s Thm prescribes how to set reserves on VCG. [see Ostrovsky and Schwarz, EC’11] Ingredients of the proof: 1) study two cases: (i) revenue is distributed among many slots (ii) most of the revenue comes from one slot 2) passing to virtual values 3) prophet inequalities
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Revenue Welfare
Opt Welfare Opt Revenue
How does the plot of all equilibria look like? Is there an equilibrium achieving maximum revenue and social welfare ? ?
Revenue-Efficiency Trade offs
Now in the non-Bayesian world, where are fixed:
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Observation: The revenue optimal equilibrium might be inefficient.
1.2 1.0
Cost of efficiency: ratio between revenue-optimal equilibrium and revenue-
- ptimal efficient
- equilibrium. For vector:
Revenue-Efficiency Trade offs
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Thm 3: If CTR α are convex, then the revenue-
- ptimal equilibrium is efficient.
Observation: The revenue optimal equilibrium might be inefficient.
i α1 α2 α3 α4 α5
Revenue Welfare
Revenue-Efficiency Trade offs
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Thm 3: If CTR α are convex, then the revenue-
- ptimal equilibrium is efficient.
Proof Idea:
- Structure of revenue in inefficient equilibria
- Local improvement proof
Revenue-Efficiency Trade offs
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- Bounds on revenue extracted by GSP
– Full Information – Bayesian setting – Revenue x Welfare tradeoffs
Conclusion
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- Bounds on revenue extracted by GSP