e-commerce lab, csa, iisc 1 game theoretic problems in network economics and mechanism design...
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E-Commerce Lab, CSA, IISc1
Game Theoretic Problems in Network Economics and
Mechanism Design Solutions
Y. Narahari
Co-Researchers: Dinesh Garg, Rama Suri, Hastagiri,
Sujit Gujar
September 2007
E-Commerce LabComputer Science and Automation,
Indian Institute of Science, Bangalore
E-Commerce Lab, CSA, IISc2
OUTLINE1. Examples of Game Theoretic Problems in Network
Economics
2. Mechanism Design
3. Case Study: Sponsored Search Auctions
4. Future Work
E-Commerce Lab, CSA, IISc3
Talk Based on
Y. Narahari, Dinesh Garg, Rama Suri, Hastagiri
Game Theoretic Problems in Network Economics and Mechanism Design
Solutions
Research Monograph in the AI & KP Series
To Be Published by
Springer, London, 2008
E-Commerce Lab, CSA, IISc4
Supply Chain Network Formation
1X 2X3X 4X
n
iiXY
1
Supply Chain Network Planner
Stage Manager
E-Commerce Lab, CSA, IISc5
Indirect Materials ProcurementIndirect Materials Procurement
PROC.MARKET
Suppliers with Volume Contracts
Catalogued Suppliers withoutVolume Contracts
Non CataloguedSuppliers
PReqs
PO’s to Suppliers
RFQ
Quotes
Auction
IIScIISc
EEEE
CSACSA
PHYPHY
ADMADM
Purchase Reqs
Reqs PURCHASESYSTEM
OptimizedOrder(s) recommendations
Vendor identified
E-Commerce Lab, CSA, IISc6
Ba
sed
on
Typ
e o
f A
pp
lica
tion
Or
pro
du
ct,
pro
ble
ms
are
d
istr
ibu
ted
to
va
riou
s Q
ue
ue
s
Ticket Allocation in Software Maintenance
Customer
.
.
.
Web Interface
Product Maintenance Processes
Product #1Queue
Product #100Queue
.
.
.
Level 1
Team of Maintenance Engineers
Product Lead #1
Product Lead #100
.
.
.
.
.
.
E-Commerce Lab, CSA, IISc7
Ticket Allocation Game
Project lead (Ticket Allocator) (rational and intelligent)
Maintenance Engineers (rational and intelligent)
effort, time
effort, time
effort, time
E-Commerce Lab, CSA, IISc8
Resource Allocation in Grid Computing
E-Commerce Lab, CSA, IISc9
?
Incentive Compatible Broadcast in Ad hoc Wireless Networks
E-Commerce Lab, CSA, IISc10
Tier 1
Tier 2
Tier 3
Tier 1: UU Net, Sprint, AT&T, Genuity
Tier 2: Regional/National ISPs
Tier 3: Residential/Company ISP
Internet Routing
E-Commerce Lab, CSA, IISc11
Web Service Composition
There could be alternate service providers foreach web service
How do we select the best mix of web service providersso as to execute the end-to-end business process at
minimum cost taking into account QOS requirements?
A B C
Web Service
Web Service
Web Service
Service Providers1, 2
Service Providers 2,3
Service Providers 3,4
E-Commerce Lab, CSA, IISc12
Web Services Composition Game
Web Service Requestor (client) (rational and intelligent)
Web Service Providers (rational and intelligent)
A, B, AB
A, B, C
A, C, AC
A, B, C, ABC
1
2
3
4
E-Commerce Lab, CSA, IISc13
Web Services Market Game
Web Services
Market
QoS SLA Cost Penalties
Web Service Providers
Web Service Requestors
(rational and intelligent) (rational and intelligent)
E-Commerce Lab, CSA, IISc14
Sponsored Search Auction
E-Commerce Lab, CSA, IISc15
Sequence of Queries
User 1
User 2
User N
Q1 Q2 Q1 Q3 Q2 Q1 Q2 Q3
E-Commerce Lab, CSA, IISc16
Sponsored Search Auction Game
AdvertisersCPC
1
2
n
E-Commerce Lab, CSA, IISc17
Some Important Observations
Playersare rational and intelligent
Some information is common knowledge
Conflict and cooperationare both relevant issues
Some information is is private and distributed(incomplete information)
Our Objective: Design a social choice functionWith desirable properties, given that the
players are rational, intelligent, and strategic
E-Commerce Lab, CSA, IISc18
Game Theory
• Mathematical framework for rigorous study of conflict and cooperation among rational, intelligent agents
Market
Buying Agents (rational and intelligent)
Selling Agents (rational and intelligent)
E-Commerce Lab, CSA, IISc19
Strategic form Games
S1
Sn
U1 : S R
Un : S R
N = {1,…,n}
Players
S1, … , Sn
Strategy Sets
S = S1 X … X Sn
Payoff functions
(Utility functions)
• Players are rational : they always strive to maximize their individual payoffs
• Players are intelligent : they can compute their best responsive strategies
• Common knowledge
E-Commerce Lab, CSA, IISc20
Example 1: Matching Pennies
• Two players simultaneously put down a coin, heads up or tails up. Two-Player zero-sum game
S1 = S2 = {H,T}
(1,-1) (-1,1)
(-1,1) (1,-1)
E-Commerce Lab, CSA, IISc21
Example 2: Prisoners’ Dilemma
E-Commerce Lab, CSA, IISc22
Example 3: Hawk - Dove
2
1
H
Hawk
D
Dove
H
Hawk 0,0 20,5
D
Dove 5,20 10,10
Models the strategic conflict when two players are fighting over a company/territory/property, etc.
E-Commerce Lab, CSA, IISc23
Example 4: Indo-Pak Budget Game
Pak
India
Healthcare Defence
Healthcare
10,10 -10, 20
Defence
20, -10 0,0
Models the strategic conflict when two players have to choose their priorities
E-Commerce Lab, CSA, IISc24
Example 5: Coordination
• In the event of multiple equilibria, a certain equilibrium becomes a focal equilibrium based on certain environmental factors
College MG Road
College
100,100 0,0MG Road
0,0 5,5
E-Commerce Lab, CSA, IISc25
Nash Equilibrium
• (s1*,s2
*, … , sn*) is a Nash equilibrium if si
* is a best response for player ‘i’ against the other players’ equilibrium strategies
(C,C) is a Nash Equilibrium. In fact, it is a strongly dominant strategy equilibrium
Prisoner’s Dilemma
E-Commerce Lab, CSA, IISc26
Mixed strategy of a player ‘i’ is a probability distribution on Si
is a mixed strategy Nash equilibrium if
is a best response against ,
Nash’s Theorem
Every finite strategic form game has at least one mixed strategy Nash equilibrium
*i *
i
**2
*1 ,...,, n
ni ,...,2,1
E-Commerce Lab, CSA, IISc27
John von Neumann(1903-1957)
Founder of Game theory with Oskar Morgenstern
E-Commerce Lab, CSA, IISc28
Landmark contributions to Game theory: notions of Nash Equilibrium and Nash Bargaining
Nobel Prize : 1994
John F Nash Jr. (1928 - )
E-Commerce Lab, CSA, IISc29
Defined and formalized Bayesian GamesNobel Prize : 1994
John Harsanyi (1920 - 2000)
E-Commerce Lab, CSA, IISc30
Reinhard Selten(1930 - )
Founding father of experimental economics and bounded rationalityNobel Prize : 1994
E-Commerce Lab, CSA, IISc31
Pioneered the study of bargaining and strategic behaviorNobel Prize : 2005
Thomas Schelling(1921 - )
E-Commerce Lab, CSA, IISc32
Robert J. Aumann(1930 - )
Pioneer of the notions of common knowledge, correlated equilibrium, and repeated games
Nobel Prize : 2005
E-Commerce Lab, CSA, IISc33
Lloyd S. Shapley(1923 - )
Originator of “Shapley Value” and Stochastic Games
E-Commerce Lab, CSA, IISc34
Inventor of the celebrated Vickrey auction Nobel Prize : 1996
William Vickrey(1914 – 1996 )
E-Commerce Lab, CSA, IISc35
Roger Myerson(1951 - )
Fundamental contributions to game theory, auctions, mechanism design
E-Commerce Lab, CSA, IISc36
MECHANISM DESIGN
E-Commerce Lab, CSA, IISc37
Mechanism Design Problem
1. How to transform individual preferences into social decision?2. How to elicit truthful individual preferences ?
O: OpenerM: Middle-orderL: Late-orderGreg
Yuvraj Dravid Laxman
O<M<L L<O<M M<L<O
E-Commerce Lab, CSA, IISc38
The Mechanism Design Problem agents who need to make a collective choice from outcome set
Each agent privately observes a signal which determines preferences
over the set
Signal is known as agent type.
The set of agent possible types is denoted by
The agents types, are drawn according to a probability
distribution function
Each agent is rational, intelligent, and tries to maximize its utility function
are common knowledge among the agents
i s'iiX
Xn
i si '
s'ii
n ,,1(.)
ii Xu :
(.),(.),,,,(.), nn uu 11
E-Commerce Lab, CSA, IISc39
Two Fundamental Problems in Designing a Mechanism
Preference Aggregation Problem
Information Revelation (Elicitation) Problem
For a given type profile of the agents, what outcome
should be chosen ?
n ,,1 Xx
How do we elicit the true type of each agent , which is his
private information ? i i
E-Commerce Lab, CSA, IISc40
1 2 n
2 n
1 2n
1
Xf n 1:
11 Xu :
11 ,xu
22 Xu : nn Xu :
Xx nfx ˆ,,ˆ 1
22 ,xu nn xu ,
Information Elicitation Problem
E-Commerce Lab, CSA, IISc41
1 2 n
2 n
1 2n
1
Xf n 1:
Xx nfx ,,1
Preference Aggregation Problem (SCF)
E-Commerce Lab, CSA, IISc42
1 2 n
2 n
1c 2c nc
1
XCCg n 1:
11 Xu : 22 Xu : nn Xu :
1C 2C nC
Xx nccgx ,,1
11 ,xu 22 ,xu nn xu ,
Indirect Mechanism
E-Commerce Lab, CSA, IISc43
Social Choice Function and Mechanism
f(f(θθ11, …,, …,θθnn))
θθ11 θθnn
XXЄЄ
SS11
g(sg(s11(.), …,s(.), …,snn()()
SSnn
XXЄЄ
x = (yx = (y11((θθ), …, y), …, ynn((θθ), t), t11((θθ), …, ), …, ttnn((θθ))))
(S(S11, …, S, …, Snn, g(.)), g(.))
A mechanism induces a Bayesian game and is A mechanism induces a Bayesian game and is designed to implement a social choice function in an designed to implement a social choice function in an equilibrium of the game.equilibrium of the game.
Outcome Outcome SetSet
Outcome SetOutcome Set
E-Commerce Lab, CSA, IISc44
Equilibrium of Induced Bayesian Game
iiiiii
iiiiiiiiiidii
SsSsNi
ssgussgu
,,,
))),(),((())),(),(((
A pure strategy profile is said to be dominant strategy equilibrium if
(.)(.),1dn
d ss
iiii
iiiiiiiiiiiiii
SsNi
ssguEssguEii
,,
]|))),(),((([]|))),(),((([ ***
)()(
A pure strategy profile is said to be Bayesian Nash equilibrium
(.)(.), **1 nss
Dominant Strategy-equilibrium Bayesian Nash- equilibrium
Dominant Strategy Equilibrium (DSE)
Bayesian Nash Equilibrium (BNE)
Observation
E-Commerce Lab, CSA, IISc45
Implementing an SCF
We say that mechanism implements SCF in dominant strategy equilibrium if
),,( ),,()(),( 1111 nnndn
d fssg
NiiCgM )((.), Xf :
),,( ),,()(),( 11*
1*1 nnnn fssg
We say that mechanism implements SCF in Bayesian Nash equilibrium if
NiiCgM )((.), Xf :
Andreu Mas Colell, Michael D. Whinston, and Jerry R. Green, “Microeconomic
Theory”, Oxford University Press, New York, 1995.
Dominant Strategy-implementation Bayesian Nash- implementation Observation
Bayesian Nash Implementation
Dominant Strategy Implementation
E-Commerce Lab, CSA, IISc46
Properties of an SCF Ex Post Efficiency
For no profile of agents’ type does there exist an
such that and for some
n ,,1 Xx
ifuxu iiii ),(, iiii fuxu ),(, i
Dominant Strategy Incentive Compatibility (DSIC)
Bayesian Incentive Compatibility (BIC)
Nis iiiidi ,,)(
If the direct revelation mechanism has a dominant
strategy equilibrium in which
NiifD )((.),
(.))(.),( 1dn
d ss
Nis iiiii ,,)(*
If the direct revelation mechanism has a Bayesian
Nash equilibrium in which
NiifD )((.),(.))(.),( **
1 nss
E-Commerce Lab, CSA, IISc47
Outcome Set
Project Choice Allocation
I0, I1,…, In : Monetary Transfers
x = (k, I0, I1,…, In )
K = Set of all k
X = Set of all x
E-Commerce Lab, CSA, IISc48
Social Choice Function
where,
E-Commerce Lab, CSA, IISc49
Values and Payoffs
Quasi-linear Utilities
E-Commerce Lab, CSA, IISc50
11 Xu : 22 Xu : nn Xu :
Xx
1 2 n
2 n1(.)1 (.)2 (.)n
Policy Maker
Quasi-Linear Environment
011
iiin tnitKkttkX ,,, ,|),,,(
11111 tkvxu ),(),(
project choice Monetary transfer to agent 1
Valuation function of agent 1
E-Commerce Lab, CSA, IISc51
Properties of an SCF in Quasi-Linear Environment
Ex Post Efficiency Dominant Strategy Incentive Compatibility (DSIC) Bayesian Incentive Compatibility (BIC) Allocative Efficiency (AE)
Budget Balance (BB)
SCF is AE if for each , satisfies(.)),(.),(.),((.) nttkf 1 )(k
n
iii
Kkkvk
1
),(maxarg)(
SCF is BB if for each , we have(.)),(.),(.),((.) nttkf 1
01
n
iit )(
Lemma 1An SCF is ex post efficient in quasi-linear
environment iff it is AE + BB
(.)),(.),(.),((.) nttkf 1
E-Commerce Lab, CSA, IISc52
A Dominant Strategy Incentive Compatible Mechanism
1. Let f(.) = (k(.),I0(.), I1(.),…, In(.)) be allocatively efficient.
2. Let the payments be :
Groves Mechanism
E-Commerce Lab, CSA, IISc53
VCG Mechanisms (Vickrey-Clarke-Groves)
Vickrey Vickrey AuctionAuction
Generalized Vickrey Generalized Vickrey AuctionAuction
Clarke MechanismsClarke Mechanisms
Groves MechanismsGroves Mechanisms
• Allocatively efficient, Allocatively efficient, individual rational, individual rational, and and dominant strategy incentive compatible with quasi-dominant strategy incentive compatible with quasi-linear utilities.linear utilities.
E-Commerce Lab, CSA, IISc54
A Bayesian Incentive Compatible Mechanism
1. Let f(.) = (k(.),I0(.), I1(.),…, In(.)) be allocatively efficient.
2. Let types of the agents be statistically independent of one another
3.
dAGVA Mechanism
E-Commerce Lab, CSA, IISc55
Basic Types of Procurement Auctions
11
nn
0, 10, 20, 30,0, 10, 20, 30,
40, 45, 50, 55,40, 45, 50, 55,
58, 60, stop.58, 60, stop.BuyerBuyer
SellersSellers
Winner = 4 Winner = 4 Price = 60Price = 60
11
22
33
44
Reverse Dutch AuctionReverse Dutch Auction
Reverse Second Price Auction Reverse Second Price Auction (Reverse Vickrey Auction)(Reverse Vickrey Auction)
Winner = 4 Winner = 4 Price = 60Price = 60
11
22
33
44
7575
Reverse First Price AuctionReverse First Price Auction
7070
6060
8080 7575
6565
6060
5050
11
nn
100, 95, 90, 100, 95, 90, 85,85,
80, 75, 70, 65,80, 75, 70, 65,
60, stop.60, stop.AuctioneerAuctioneer oror BuyerBuyer
Reverse English AuctionReverse English Auction
SellersSellers
SellersSellers SellersSellers
E-Commerce Lab, CSA, IISc56
BIC
AE
WBB
IR
SBB
dAGVA
DSIC
EPE
GROVES
MOULIN
E-Commerce Lab, CSA, IISc57
Sponsored Search Auctions
E-Commerce Lab, CSA, IISc58
OUTLINE
Sponsored Search Auctions
SSA as a Mechanism Design Problem
Three Different Auction Mechanisms: GFP, GSP, VCG
A New Mechanism: OPT
Comparison of Different Mechanisms
Ongoing Work
E-Commerce Lab, CSA, IISc59
Sponsored Search Auction Game
AdvertisersCPC
1
2
n
E-Commerce Lab, CSA, IISc60
Some Important Observations
Playersare rational and intelligent
Some information is common knowledge
Conflict and cooperationare both relevant issues
Some information is is private and distributed(incomplete information)
Our Objective: Design a social choice functionWith desirable properties, given that the
players are rational, intelligent, and strategic
E-Commerce Lab, CSA, IISc61
1 2 n
)ˆ( )ˆ( )ˆ( ))ˆ(( ),ˆ(m
1j
iiijjiiiii pypyvfu
2 n
1 2 n
MjNiiij pyf
, )ˆ( ,)ˆ( )ˆ(
(Allocation Rule, Payment Rule)
1
Sponsored Search Auction as a Mechanism Design Problem
iiis :
E-Commerce Lab, CSA, IISc62
1 2 N
2 N
1 2 N
1
Xf N 1:
X
11 Xu :
22 Xu : NN Xu :
E-Commerce Lab, CSA, IISc63
1 2 N
2 N
1c 2c Nc
1
XCCg N 1:
X
11 Xu :
22 Xu : NN Xu :
1C 2C NC
E-Commerce Lab, CSA, IISc64
Bayesian Game Induced by the Auction Mechanism
NiiiNiiNiib uN )((.),,)(,)(,
Nwhere
)),ˆ((),( iiii fuu
Mechanism Niif )((.), Induces a Bayesian game
among advertisers
i
i
iiis :
(.)i
Set of advertisers
Valuation set of advertiser
Set of bids for advertiser
A pure strategy of advertiser
Prior distribution of advertiser valuations
Utility payoff of advertiser
i
i
,i
i
ii Ss
si '
E-Commerce Lab, CSA, IISc65
Strategic Bidding Behavior of Advertisers
If all the advertisers are rational and intelligent and this fact is common knowledge then each advertiser’s expected bidding behavior is given by
Bayesian Nash Equilibrium
iiiiiiiiiiiiii sfuEssfuEii
i*** ˆ |))),(,ˆ((|))),(),(((
Strategy profile is said to be Bayesian Nash equilibrium iff (.),(.), **nss 1
Dominant Strategy Equilibrium
Strategy profile is said to be Dominant Strategy equilibrium iff
(.),(.), **nss 1
iiiiiiiiiii fusfu i-i* ˆ ,ˆ ))),ˆ,ˆ(( ))),ˆ),(((
E-Commerce Lab, CSA, IISc66
Advertisers’ Bidding StrategyVCG: Follow irrespective of what the others are doing iiis )(*
OPT: Follow if all rivals are also doing so iiis )(*
GSP: Never follow strategy . Use the followingiiis )(*
i
l
i
l
nmdxxsmxfmg
mndxxsnxfng
s
ii
i
ii
i
ii
if: )('),,(),(
if : )('))(,,())(,(
)(*
1
11
1
k
j
jni
jij
nji Cjkxf
1
21
11 ))(())(()(),,(
1
1
1111
111k
j
jni
jij
njj
kni
kik
nki CjCkkg ))(())(()( ))(())((),(
E-Commerce Lab, CSA, IISc67
Properties of a Sponsored Search Auction Mechanism
E-Commerce Lab, CSA, IISc68
Google’s Objectives
Q1 Q2 Q1 Q3 Q3Q1 Q2 Q1 Q3 Q3
Short Term Long Term
Revenue Maximization
Click Fraud Resistance
Individual Rationality
Incentive Compatibility
E-Commerce Lab, CSA, IISc69
Revenue Maximization
Google’s Objectives
Choose auction mechanism Niif )((.), such that despite
strategic bidding behavior of advertisers, expected revenue is maximum
Click Fraudulence
increase the spending of rival advertisers without increasing its own.
Niif )((.), is click fraudulent if an advertiser finds a way to
Click Fraud Resistance
Niif )((.), is click fraud resistant If it is not click fraudulent
E-Commerce Lab, CSA, IISc70
Google’s Objectives Individual Rationality
• Advertiser’s participation is voluntary
• Will bid only if the participation constraint is satisfied
iiiiiiii fuEfUi
)|),(()|( 0
Why should bother about it ?
Advertisers may decide to quit !!
What can do about it ?
Choose an auction mechanism Niif )((.), which is IR
E-Commerce Lab, CSA, IISc71
Incentive Compatibility
Google’s Objectives
In practice, the assumptions like rationality, intelligence, and common knowledge are hardly true
Need to invoke sophisticated but impractical software agents to
compute the optimal (.)*is
Difficulties faced by an Advertiser
Why should bother about it ?
Low ROI switch to other search engines !!
E-Commerce Lab, CSA, IISc72
Incentive CompatibilityWhat can do about it ?
Choose an auction mechanism Niif )((.), which is IC
Dominant Strategy Incentive Compatibility
Bayesian Incentive Compatibility
Incentive compatible if truth telling is a dominant strategy equilibrium
Auction mechanism Niif )((.), is said to be dominant strategy
iiiiiiiiii fufu i-iˆ ,ˆ ))),ˆ,ˆ(( ))),ˆ,((
compatible if truth telling is a Bayesian Nash equilibrium
Auction mechanism Niif )((.), is said to be Bayesian incentive
iiiiiiiiiii fufuEi
i |))),,ˆ((E |))),,((i-
E-Commerce Lab, CSA, IISc73
Properties of Auction Mechanisms
Bayesian IC
• GFP• GSP
DominantStrategy
IndividualRationality
IC • VCG
• OPT
E-Commerce Lab, CSA, IISc74
Four Different Auction Mechanisms
GFP GSP VCG OPT
(Overture, 1997) (Google, 2002)
Notation
position in Ad ofy probabilit Click
click per for advertiser from charged is that Price)(
o/w
slot allocated is advertiser if )(
bids the of ordering Decreasing ,,
sadvertiser of vector Bid ,,)((1)
ththij
i
ij
n
n
ji
ip
jiy
0
1
1
Feasibility Condition: niimii ,, 11 21
E-Commerce Lab, CSA, IISc75
Allocation Rule
Payment Rule
Allocated the slots in decreasing order of bids
Every time a user clicks on the Ad, the advertiser’s account is automatically billed the amount of the advertiser’s bid
Generalized First Price (GFP)
1
2
m
)(1
)(2
)(m
)(1)(2
)(m
E-Commerce Lab, CSA, IISc76
Example: GFP
Search Results Sponsored Links
Q
1
2
021 .
512 .
013 .
2015102
0015102
1015102
1
12
11
).,.,.(
).,.,.(
).,.,.(
p
y
y
51015102
1015102
0015102
2
22
21
.).,.,.(
).,.,.(
).,.,.(
p
y
y
0015102
0015102
0015102
3
32
31
).,.,.(
).,.,.(
).,.,.(
p
y
y
E-Commerce Lab, CSA, IISc77
Allocation Rules
Allocate the slots in decreasing order of bids
Generalized Second Price (GSP)
1
2
m
)(1
)(2
)(m Rule:
Greedy Rule: Allocate 1st slot to advertiser
Rule:
Allocate the slots in decreasing order of Ranking Score
Ranking Score =
iiNi
i 11
maxarg
ii CTR
Allocate 2nd slot to advertiser iiiNi
i 121\
maxarg
E-Commerce Lab, CSA, IISc78
Generalized Second Price (GSP) Greedy
nnnmn
m
CTR
CTR
11
1
111
Observation 1:
Mjnjjj 21 Greedy Click probability is independent of the
identity of advertisers Greedy
E-Commerce Lab, CSA, IISc79
Generalized Second Price (GSP) Payment Rule
)(1)(2
)(m
For every click, charge next highest bid + $0.01
The bottom most advertiser is charged highest
disqualified bid +$0.01
charge 0 if no such bid
E-Commerce Lab, CSA, IISc80
Example: GSP
Search Results Sponsored Links
Q
1
2
021 .
512 .
013 .
51015102
0015102
1015102
1
12
11
.).,.,.(
).,.,.(
).,.,.(
p
y
y
1015102
1015102
0015102
2
22
21
).,.,.(
).,.,.(
).,.,.(
p
y
y
0015102
0015102
0015102
3
32
31
).,.,.(
).,.,.(
).,.,.(
p
y
y
E-Commerce Lab, CSA, IISc81
Vickrey-Clarke-Groves (VCG)Allocation Rule
In decreasing order of bids1
2
m
)(1
)(2
)(m
)(1)(2
)(m
Payment Rule
Case 1
)( mn
Case 2 )( nm
)(,, )( 111 1
11
nip
n
ijjjj
ii
0np
)(,, )( 111 1
11
mip
n
ijjjj
ii
)( 1 mmp
nmipi ,),( 10
E-Commerce Lab, CSA, IISc82
Example: VCG
Search Results Sponsored Links
Q
1
2
021 .
512 .
013 .
1
21
12
11
151015102
0015102
1015102
.).,.,.(
).,.,.(
).,.,.(
p
y
y
1015102
1015102
0015102
2
22
21
).,.,.(
).,.,.(
).,.,.(
p
y
y
0015102
0015102
0015102
3
32
31
).,.,.(
).,.,.(
).,.,.(
p
y
y
E-Commerce Lab, CSA, IISc83
Allocation Rule
OPT
Optimal (OPT)Allocation Rule 1
2
m
)(1
)(2
)(m
o/w
if
if
0 if
:
:
:
:
,,
,,
,
)(
)(i
jii
jii
i
ij JJ
JJ
J
mnj
nmj
mj
y
1
1
1
0
1
1
0
Where is the highest value among )( jJthj
)(
)()(
ii
iiiiiJ
1
Observation 4:
Advertisers are symmetric i.e.
(.)(.)(.) n
n
21
21
(Assumption: is non decreasing: True for Uniform, Exponential))( iiJ
E-Commerce Lab, CSA, IISc84
Optimal (OPT)Payment Rule Assumptions:
1. Advertisers are symmetric, i.e.
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E-Commerce Lab, CSA, IISc85
Example: OPT
Search Results Sponsored Links
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E-Commerce Lab, CSA, IISc86
Example: OPT
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E-Commerce Lab, CSA, IISc87
Example: OPT
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E-Commerce Lab, CSA, IISc88
Expected Revenue of Seller
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OPTVCG RR Observation
E-Commerce Lab, CSA, IISc89
Expected Revenue of SellerCase 1 mn
E-Commerce Lab, CSA, IISc90
Conclusions
Allocation Payment DSIC BIC IRCFR
GSPDecreasing order of the
bids
Next Highest bid
(PPC)X X X
VCGDecreasing order of the
bids
Marginal Contribution
(PPC)X
OPTDecreasing order of the
bids(PPP) X
E-Commerce Lab, CSA, IISc91
Ongoing Work
Deeper Mechanism Design
Repeated Games Model
Learning Bidding Strategies
Cooperative Bidding
E-Commerce Lab, CSA, IISc92
Questions and Answers …
Thank You …
E-Commerce Lab, CSA, IISc93
Vickrey Auction for Ticket Allocation
Project lead Ticket Allocator
Maintenance Engineers
effort, time
effort, time
effort, time
E-Commerce Lab, CSA, IISc94
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Incentive Compatible Broadcast Problem: Successful broadcast requires appropriate forwarding of the packets by individual selfish wireless nodes. Reimbursing the forwarding costs incurred by the nodes is a way to make them forward the packets. For this, we need to know the exact transit costs of the nodes. We can design an incentive compatible broadcast protocol by embedding appropriate incentive schemes into the broadcast protocol. We shall refer to the problem of designing such robust broadcast protocols as the incentive compatible broadcast (ICB) problem.
Bi-connected ad hoc network
Source Rooted Broadcast Tree
Line Network
E-Commerce Lab, CSA, IISc95
Vickrey Auction for Ticket Allocation
N = { 1, 2, 3 }Maintenance Engineers
AllocationEngineer 1 is selected as winner (lowest bid)
Bid 1 – Rs. 1000Bid 2 – Rs. 1500Bid 3 – Rs. 1200
PaymentEngineer 1 is paid
1000 + (1200 – 1000)= 1200
Vickrey Auction is Dominant Strategy Incentive Compatible --
Truth revelation is a best response for each agentIrrespective of what is reported by the other agents
E-Commerce Lab, CSA, IISc96
Vickrey Auction as a Strategic Form Game
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E-Commerce Lab, CSA, IISc97
GVA for Web Services Composition
Web Service Requestor (client)
Web Service Providers
A, B, AB
A, B, C
A, C, AC
A, B, C, ABC
1
2
3
4
E-Commerce Lab, CSA, IISc98
GVA for Web Services Composition
A B C AB AC ABC
1 30 20 - 40 - -
2 25 25 25 - - -
3 35 - 25 - 50 -
4 30 30 20 - - 70
• Optimal Allocation: 1AB; 4 C• Optimal Cost: 40 + 20 = 60• Optimal Cost without 1 = 70• Optimal Cost without 4 = 65• Payment to provider 1 = 40 + 70 – 60 = 50• Payment to provider 4 = 20 + 65 - 60 = 25