Download presentation

Presentation is loading. Please wait.

Published byIsabella Georgeson Modified over 2 years ago

1
Performance Evaluation Sponsored Search Markets Giovanni Neglia INRIA – EPI Maestro 4 February 2013

2
Google r A class of games for which there is a function P(s 1,s 2,…s N ) such that m For each i U i (s 1,s 2,…x i,…s N )>U i (s 1,s 2,…y i,…s N ) if and only if P(s 1,s 2,…x i,…s N )>P(s 1,s 2,…y i,…s N ) r Properties of potential games: Existence of a pure-strategy NE and convergence to it of best-response dynamics r The routing games we considered are particular potential games

3
How it works r Companies bid for keywords r On the basis of the bids Google puts their link on a given position (first ads get more clicks) r Companies are charged a given cost for each click (the cost depends on all the bids)

4
Some numbers r ≈ 95% of Google revenues (46 billions$) from ads m investor.google.com/financial/tables.html m 87% of Google-Motorola revenues (50 billions$) r Costs m "calligraphy pens" $1.70 m "Loan consolidation" $50 m "mesothelioma" $50 per click r Click fraud problem

5
Outline r Preliminaries m Auctions m Matching markets r Possible approaches to ads pricing r Google mechanism r References m Easley, Kleinberg, "Networks, Crowds and Markets", ch.9,10,15

6
Types of auctions r 1 st price & descending bids r 2 nd price & ascending bids

7
Game Theoretic Model r N players (the bidders) r Strategies/actions: b i is player i’s bid r For player i the good has value v i r p i is player i’s payment if he gets the good r Utility: m v i -p i if player i gets the good m 0 otherwise r Assumption here: values v i are independent and private m i.e. very particular goods for which there is not a reference price

8
Game Theoretic Model r N players (the bidders) r Strategies: b i is player i’s bid r Utility: m v i -b i if player i gets the good m 0 otherwise r Difficulties: m Utilities of other players are unknown! m Better to model the strategy space as continuous m Most of the approaches we studied do not work!

9
2 nd price auction r Player with the highest bid gets the good and pays a price equal to the 2 nd highest bid r There is a dominant strategies m I.e. a strategy that is more convenient independently from what the other players do m Be truthful, i.e. bid how much you evaluate the good (b i =v i ) m Social optimality: the bidder who value the good the most gets it!

10
b i =v i is the highest bid bids bibi bkbk bhbh bnbn Bidding more than v i is not convenient U i =v i -b k >v i -b i =0 bids b i ’>b i bkbk bhbh bnbn U i ’=v i -b k

11
b i =v i is the highest bid bids bibi bkbk bhbh bnbn Bidding less than v i is not convenient (may be unconvenient) U i =v i -b k >v i -b i =0 bids b i ’**
{
"@context": "http://schema.org",
"@type": "ImageObject",
"contentUrl": "http://images.slideplayer.com/11/3189419/slides/slide_11.jpg",
"name": "b i =v i is the highest bid bids bibi bkbk bhbh bnbn Bidding less than v i is not convenient (may be unconvenient) U i =v i -b k >v i -b i =0 bids b i ’ v i -b i =0 bids b i ’
**

12
b i =v i is not the highest bid bids bkbk bibi bhbh bnbn Bidding more than v i is not convenient (may be unconvenient) U i =0 bids b i ’>b i bkbk bhbh bnbn U i ’=v i -b k

13
b i =v i is not the highest bid bids bkbk bibi bhbh bnbn Bidding more than v i is not convenient U i =0 bids b i ’**
{
"@context": "http://schema.org",
"@type": "ImageObject",
"contentUrl": "http://images.slideplayer.com/11/3189419/slides/slide_13.jpg",
"name": "b i =v i is not the highest bid bids bkbk bibi bhbh bnbn Bidding more than v i is not convenient U i =0 bids b i ’
**

14
Seller revenue r N bidders r Values are independent random values between 0 and 1 r Expected i th largest utility is (N+1-i)/(N+1) r Expected seller revenue is (N-1)/(N+1)

15
1 st price auction r Player with the highest bid gets the good and pays a price equal to her/his bid r Being truthful is not a dominant strategy anymore! r How to study it?

16
1 st price auction r Assumption: for each player the other values are i.i.d. random variables between 0 and 1 m to overcome the fact that utilities are unknown r Player i’s strategy is a function s() mapping value v i to a bid b i m s() strictly increasing, differentiable function 0≤s(v)≤v s(0)=0 We investigate if there is a strategy s() common to all the players that leads to a Nash equilibrium

17
1 st price auction r Assumption: for each player the other values are i.i.d. random variables between 0 and 1 r Player i’s strategy is a function s() mapping value v i to a bid b i Expected payoff of player i if all the players plays s(): U i (s,…s,…s) = v i N-1 (v i -s(v i )) prob. i wins i’s payoff if he/she wins

18
1 st price auction Expected payoff of player i if all the players play s(): U i (s,…s,…s) = v i N-1 (v i -s(v i )) What if i plays a different strategy t()? If all players playing s() is a NE, then : U i (s,…s,…s) = v i N-1 (v i -s(v i )) ≥ v i N-1 (v i -t(v i )) = = U i (s,…t,…s) Difficult to check for all the possible functions t() different from s() Help from the revelation principle

19
The Revelation Principle All the strategies are equivalent to bidder i supplying to s() a different value of v i s() vivi bibi t() vivi bi'bi' s() vi'vi' bi'bi'

20
1 st price auction Expected payoff of player i if all the players plays s(): U i (v 1,…v i,…v N ) = U i (s,…s,…s) = v i N-1 (v i -s(v i )) What if i plays a different strategy t()? By the revelation principle: U i (s,…t,…s) = U i (v 1,…v,…v N ) = v N-1 (v i -s(v)) If v i N-1 (v i -s(v i )) ≥ v N-1 (v i -s(v)) for each v (and for each v i ) Then all players playing s() is a NE

21
1 st price auction If v i N-1 (v i -s(v i )) ≥ v N-1 (v i -s(v)) for each v (and for each v i ) Then all players playing s() is a NE f(v)=v i N-1 (v i -s(v i )) - v N-1 (v i -s(v)) is minimized for v=v i f’(v)=0 for v=v i, i.e. (N-1) v i N-2 (v i -s(v)) + v i N-1 s’(v i ) = 0 for each v i s’(v i ) = (N-1)(1 – s(v i )/v i ), s(0)=0 Solution: s(v i )=(N-1)/N v i

22
1 st price auction r All players bidding according to s(v) = (N-1)/N v is a NE r Remarks m They are not truthful m The more they are, the higher they should bid r Expected seller revenue m (N-1)/N E[v max ] = (N-1)/N N/(N+1) = (N-1)/(N+1) m Identical to 2 nd price auction! m A general revenue equivalence principle

23
Outline r Preliminaries m Auctions m Matching markets r Possible approaches to ads pricing r Google mechanism r References m Easley, Kleinberg, "Networks, Crowds and Markets", ch.9,10,15

24
Matching Markets 1 2 3 1 2 3 v 11, v 21, v 31 v 12, v 22, v 32 How to match a set of different goods to a set of buyers with different evaluations v ij : value that buyer j gives to good i goods buyers

25
Matching Markets 1 2 3 1 2 3 12, 4, 2 8, 7, 6 7, 5, 2 How to match a set of different goods to a set of buyers with different evaluations p 1 =2 p 2 =1 p 3 =0 Which goods buyers like most? Preferred seller graph

26
Matching Markets 1 2 3 1 2 3 12, 4, 2 8, 7, 6 7, 5, 2 p 1 =2 p 2 =1 p 3 =0 Which goods buyers like most? Preferred seller graph r Given the prices, look for a perfect matching on the preferred seller graph r There is no such matching for this graph

27
Matching Markets 1 2 3 1 2 3 12, 4, 2 8, 7, 6 7, 5, 2 p1=3p1=3 p 2 =1 p 3 =0 Which goods buyers like most? Preferred seller graph r But with different prices, there is

28
Matching Markets 1 2 3 1 2 3 12, 4, 2 8, 7, 6 7, 5, 2 p1=3p1=3 p 2 =1 p 3 =0 Which goods buyers like most? Preferred seller graph r But with different prices, there is r Such prices are market clearing prices

29
Market Clearing Prices r They always exist m And can be easily calculated if valuations are known r They are socially optimal in the sense that they maximize the sum of all the payoffs in the network (both sellers are buyers)

30
Outline r Preliminaries m Auctions m Matching markets r Possible approaches to ads pricing r Google mechanism r References m Easley, Kleinberg, "Networks, Crowds and Markets", ch.9,10,15

31
Ads pricing 1 2 3 1 2 3 v1v1 v2v2 v3v3 How to rank ads from different companies v i : value that company i gives to a click Ads positions companies r1r1 r2r2 r3r3 r i : click rate for an ad in position i (assumed to be independent from the ad and known a prior i)

32
Ads pricing as a matching market 1 2 3 1 2 3 v 1 r 1, v 1 r 2, v 1 r 3 v i : value that company i gives to a click Ads positions companies r1r1 r2r2 r3r3 r i : click rate for an ad in position i (assumed to be independent from the ad and known a prior i) v 2 r 1, v 2 r 2, v 2 r 3 v 3 r 1, v 3 r 2, v 3 r 3 r Problem: Valuations are not known! r … but we could look for something as 2 nd price auctions

33
The VCG mechanism r The correct way to generalize 2 nd price auctions to multiple goods r Vickrey-Clarke-Groves r Every buyers should pay a price equal to the social value loss for the others buyers m Example: consider a 2 nd price auction with v 1 >v 2 >…v N With 1 present the others buyers get 0 Without 1, 2 would have got the good with a value v 2 then the social value loss for the others is v 2

34
The VCG mechanism r The correct way to generalize 2 nd price auctions to multiple goods r Vickrey-Clarke-Groves r Every buyers should pay a price equal to the social value loss for the others buyers m If V B S is the maximum total valuation over all the possible perfect matchings of the set of sellers S and the set of buyers B, m If buyer j gets good i, he/she should be charged V B-j S - V B-j S-i

35
VCG example 1 2 3 1 2 3 v 1 =3 v i : value that company i gives to a click Ads positions companies r 1 =10 r 2 =5 r 3 =2 r i : click rate for an ad in position i (assumed to be independent from the ad and known a prior i) v 2 =2 v 3 =1

36
VCG example 1 2 3 1 2 3 30, 15, 6 Ads positions companies 20, 10, 4 10, 5, 2

37
VCG example 1 2 3 1 2 3 30, 15, 6 Ads positions companies 20, 10, 4 10, 5, 2 r This is the maximum weight matching r 1 gets 30, 2 gets 10 and 3 gets 2

38
VCG example 1 2 3 1 2 3 30, 15, 6 Ads positions companies 20, 10, 4 10, 5, 2 r If 1 weren’t there, 2 and 3 would get 25 instead of 12, r Then 1 should pay 13

39
VCG example 1 2 3 1 2 3 30, 15, 6 Ads positions companies 20, 10, 4 10, 5, 2 r If 2 weren’t there, 1 and 3 would get 35 instead of 32, r Then 2 should pay 3

40
VCG example 1 2 3 1 2 3 30, 15, 6 Ads positions companies 20, 10, 4 10, 5, 2 r If 3 weren’t there, nothing would change for 1 and 2, r Then 3 should pay 0

41
The VCG mechanism r Every buyers should pay a price equal to the social value loss for the others buyers m If V B S is the maximum total valuation over all the possible perfect matchings of the set of sellers S and the set of buyers B, m If buyer j gets good i, he/she should be charged V B-j S - V B-j S-i r Under this price mechanism, truth-telling is a dominant strategy

42
Outline r Preliminaries m Auctions m Matching markets r Possible approaches to ads pricing r Google mechanism r References m Easley, Kleinberg, "Networks, Crowds and Markets", ch.9,10,15

43
Google’s GSP auction r Generalized Second Price r Once all the bids are collected b 1 >b 2 >…b N r Company i pays b i+1 r In the case of a single good (position), GSP is equivalent to a 2 nd price auction, and also to VCG r But why Google wanted to implement something different???

44
GSP properties r Truth-telling may not be an equilibrium

45
GSP example 1 2 3 1 2 3 v 1 =7 v i : value that company i gives to a click Ads positions companies r 1 =10 r 2 =4 r 3 =0 r i : click rate for an ad in position i (assumed to be independent from the ad and known a prior i) v 2 =6 v 3 =1 r If each player bids its true evaluation, 1 gets a payoff equal to 10 r If 1 bids 5, 1 gets a payoff equal to 24

46
GSP properties r Truth-telling may not be an equilibrium r There is always at least 1 NE maximizing total advertiser valuation

47
GSP example 1 2 3 1 2 3 v 1 =7 v i : value that company i gives to a click Ads positions companies r 1 =10 r 2 =4 r 3 =0 r i : click rate for an ad in position i (assumed to be independent from the ad and known a prior i) v 2 =6 v 3 =1 r Multiple NE m 1 bids 5, 2 bids 4 and 3 bids 2 m 1 bids 3, 2 bids 5 and 3 bids 1

48
GSP properties r Truth-telling may not be an equilibrium r There is always at least 1 NE maximizing total advertiser valuation r Revenues can be higher or lower than VCG m Attention: the revenue equivalence principle does not hold for auctions with multiple goods! m Google was targeting higher revenues… m … not clear if they did the right choice.

49
GSP example 1 2 3 1 2 3 v 1 =7 Ads positions companies r 1 =10 r 2 =4 r 3 =0 v 2 =6 v 3 =1 r Multiple NE 1 bids 5, 2 bids 4, 3 bids 2 google’s revenue=48 1 bids 3, 2 bids 5, 3 bids 1 google’s revenue=34 r With VCG, google’s revenue=44

50
Other issues r Click rates are unknown and depend on the ad! m Concrete risk: low-quality advertiser bidding high may reduce the search engine’s revenue m Google’s solution: introduce and ad-quality factor taking into account actual click rate, relevance of the page and its ranking Google is very secretive about how to calculate it => the market is more opaque r Complex queries, nobody paid for m Usually engines extrapolate from simpler bids

Similar presentations

OK

Game Theory in Wireless and Communication Networks: Theory, Models, and Applications Lecture 6 Auction Theory Zhu Han, Dusit Niyato, Walid Saad, Tamer.

Game Theory in Wireless and Communication Networks: Theory, Models, and Applications Lecture 6 Auction Theory Zhu Han, Dusit Niyato, Walid Saad, Tamer.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on area and perimeter of quadrilaterals Ppt on emerging technologies in computer science Ppt on job rotation program Ppt on gunn diodes Ppt on congruent triangles for class 7 Ppt on world book day ideas Ppt on product specification meaning Ppt on result analysis system Ppt on trans-siberian railway route Ppt on open access