e-commerce lab, csa, iisc 1 game theoretic problems in network economics and mechanism design...

E-Commerce Lab, CSA, IISc1

Game Theoretic Problems in Network Economics and

Mechanism Design Solutions

Y. Narahari

hari@csa.iisc.ernet.in

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

Google

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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Whenever an advertiser bids charge him for every query irrespective of whether his Ad is displayed or not

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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

?

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