E-Commerce Lab, CSA, IISc1

Design of Mechanisms for Dynamic

EnvironmentsNovember 12, 2010

Y. NARAHARI

http://lcm.csa.iisc.ernet.in/hari

INDO – US WORKSHOP ON

MACHINE LEARNING, GAME THEORY, AND OPTIMIZATION

Computer Science and AutomationIndian Institute of Science, Bangalore

E-Commerce Lab, CSA, IISc2

OUTLINE

Static Mechanism Design and Our Work

Dynamic Mechanisms and Current Art

Outlook for Future and Opportunities for Collaboration

E-Commerce Lab, CSA, IISc3

Mechanism Design

Design of games / reverse engineering of games Game Engineering

Induces a game among rational and intelligentplayers such that in some equilibrium of the game,

a desired social choice function is implemented

William Vickrey Leonid Hurwicz Eric Maskin Roger Myerson

A Mechanism Without MoneyFair Division of a Cake

MotherSocial PlannerMechanism Designer

Kid 1Rational and Intelligent

Kid 2Rational and Intelligent

A Mechanism with a lot of Money

Sachin Tendulkar IPL Franchisees

1

2

3

4

Mumbai Indians

Kolkata Knight Riders

Bangalore RoyalChallengers

Punjab Lions

IPL CRICKET AUCTION

The Famous Corus Auction (31-1-2007)

CSN (Brazilian Company)

Tata Steel

US$ 12.04 Billion

Problem 1: Procurement Auctions

Buyer

SUPPLIER 1

SUPPLIER 2

SUPPLIER n

T.S. Chandrasekhar, Y. Narahari, Charlie Rosa, Pankaj Dayama, Datta Kulkarni, Jeffrey Tew. IEEE T-ASE, 2006

Supply (cost) Curves

E-Commerce Lab, CSA, IISc8

PROBLEM 2: Sponsored Search Auction Advertisers

CPC

1

2

n

D. Garg and Y. Narahari. IEEE T-ASE, 2009

A. Radhika, Y. Narahari, D. Bagchi, P. Suresh, S.V. Subrahmanya. Journal of IISc, 2010

Division n

Division 1

CCACarbon Credit

Allocator

.

Problem 3: Carbon Credit Allocator

cost

No of Carbon Credits

No of Carbon Credits

cost

E-Commerce Lab, CSA, IISc10

Problem 4: Crowdsourcing

Karthik Subbian, Ramakrishnan Kannan, Y. Narahari, IEEE APSEC, 2007

Resolve any

Dispute

Resolve any

Dispute

PayPay

CompleteComplete

AssignAssignReceive

Bids

Receive Bids

Review Problem

Review Problem

Post Problem

Post Problem

Read RespondDetermine winner

Verify Task Confirm Payment

ReadAskPlace Bids Complete Task

E-Commerce Lab, CSA, IISc11

PROPERTIES OF SOCIAL CHOICE FUNCTIONS

DSIC (Dominant Strategy

Incentive Compatibility)Reporting Truth is always good

BIC (Bayesian NashIncentive Compatibility)

Reporting truth is good wheneverothers also report truth

AE (Allocative Efficiency)Allocate items to those who

value them most

BB (Budget Balance)Payments balance receipts and

No losses are incurred

Non-DictatorshipNo single agent is favoured all

the time

Individual RationalityPlayers participate voluntarilysince they do not incur losses

E-Commerce Lab, CSA, IISc12

POSSIBILITIES AND IMPOSSIBILITIES - 1

Gibbard-Satterthwaite Theorem When the preference structure is rich,

a social choice function is DSIC iff it is dictatorial

Groves TheoremIn the quasi-linear environment, there exist social

choice functions which are both AE and DSIC

The dAGVA MechanismIn the quasi-linear environment, there exist social

choice functions which are AE, BB, and BIC

E-Commerce Lab, CSA, IISc13

POSSIBILITIES AND IMPOSSIBILITIES -2

Green- Laffont TheoremWhen the preference structure is rich, a social

choice function cannot be DSIC and BB and AE

Myerson-Satterthwaite TheoremIn the quasi-linear environment, there cannot exist

a social choice function that isBIC and BB and AE and IR

Myerson’s Optimal MechanismsOptimal mechanisms are possible subject to

IIR and BIC (sometimes even DSIC)

E-Commerce Lab, CSA, IISc14

BIC

AE

WBB

IR

SBB

dAGVA

DSIC

EPE

GROVES MYERSON

VDOPT

SSAOPT CBOPT

MECHANISM DESIGN SPACE

E-Commerce Lab, CSA, IISc15

Our work is summarized in

E-Commerce Lab, CSA, IISc16

Limitations of Classical Mechanisms

Do not model the repeated/sequential nature ofdecision making

Do not model dynamic evolution of types

Do not model dynamic populations

Do not model any learning by the agents

E-Commerce Lab, CSA, IISc17

Dynamic Mechanisms

Types could be dynamic (Dynamic type mechanisms)

Population could be dynamic(Online mechanisms)

Can capture sequential decision makingand learning

Criterion could be social welfare or revenue maximization or cost minimization

Could be with money or without money

E-Commerce Lab, CSA, IISc18

Dynamic (Type) Mechanisms Dirk Bergemann and Juuso Valimaki

The Dynamic Pivot Mechanism, Econometrica, 2010

Susan Athey and Ilya SegalAn Efficient Dynamic Mechanism, Tech Report 2007

Ruggiero Cavallo, Efficiency and Redistribution in Dynamic Mechanism Design, EC 2008

Alessandro Pavan, Ilya Segal, and Jusso ToikkaDynamic Mechanism Design: Incentive Compatibility,

Profit Maximization, Information Disclosure, 2009

Ruggiero Cavallo, David Parkes, and Satinder SinghEfficient Mechanisms with Dynamic Populations and Types,

July 2009

Topics in Game Theory Team, IISc Dynamic Mechanisms for Sponsored Search Auction, Ongoing

E-Commerce Lab, CSA, IISc19

Multi-Armed Bandit Mechanisms

Nikhil Devanur and Sham KakadeThe Price of Truthfulness for Pay-per-click Auctions, EC 2009

Moshe Babaioff, Yogeshwar Sharma, Aleksandrs SlivkinsCharacterizing Truthful MAB Mechanisms, EC 2009

Akash Das Sharma, Sujit Gujar, Y. NarahariTruthful MAB Mechanisms for Multi-slot Auctions, 2010

Sai Ming Li, Mohammad Mahdian, R. Preston McAfeeValue of Learning in Sponsored Search Auctions, WINE 2010

Sham Kakade, Ilan Lobel, and Hamid NazerzadehAn Optimal Mechanism for Multi-armed Bandit Problems, 2010

Avrim Blum and Y. Mansour. Learning, Regret Minimization, And Equilibria. In: Algorithmic Game Theory, 2007

E-Commerce Lab, CSA, IISc20

Online Mechanisms David Parkes and Satinder Singh

An MDP-Based Approach to Online Mechanism Design, NIPS’03

David Parkes, Online Mechanism DesignBook Chapter: Algorthmic Game Theory, 2007

Alex Gershkov and Benny MoldovanuDynamic Revenue Maximization with Heterogeneous Objects

American Economic Journal, 2008

Mallesh Pai and Rakesh VohraOptimal Dynamic Auctions, Kellogg Report, 2008

Florin Constantin and David Parkes, Self-correcting, Sampling-based, Dynamic Multi-unit Auctions, EC 2009

James Jou, Sujit Gujar, David Parkes, Dynamic AssignmentWithout Money, AAAI 2010

Problem 1: Procurement Auctions

Buyer

SUPPLIER 1

SUPPLIER 2

SUPPLIER n

Budget Constraints, Lead Time Constraints, Learning by Suppliers,Learning by Buyer, Logistics constraints, Combinatorial Auctions,

Cost Minimization, Multiple Attributes

Supply (cost) Curves

E-Commerce Lab, CSA, IISc22

PROBLEM 2: Sponsored Search Auction Advertisers

CPC

1

2

n

Budget Constraints, Learning by the Search Engine, Learning by theAdvertisers, Optimal Auctions

Budget constraints, Learning by the Allocator

Division n

Division 1

CCACarbon Credit

Allocator

.

Problem 3: Carbon Credit Allocator

cost

No of Carbon Credits

No of Carbon Credits

cost

E-Commerce Lab, CSA, IISc24

Problem 4: Crowdsourcing

Ticket Allocation, Group Ticket Allocation, Learning, Dynamic Population

Resolve any

Dispute

Resolve any

Dispute

PayPay

CompleteComplete

AssignAssignReceive

Bids

Receive Bids

Review Problem

Review Problem

Post Problem

Post Problem

Read RespondDetermine winner

Verify Task Confirm Payment

ReadAskPlace Bids Complete Task

Problem 5: Amazon Mechanical Turk

A Plea to Amazon: Fix Mechanical Turk! Noam Nisan’s Blog – October 21, 2010

E-Commerce Lab, CSA, IISc26

Dynamic Mechanisms: Some Generic Issues Possibility and Impossibility Results

For example: Does Green-Laffont Theorem hold for dynamic mechanisms?

Incorporate learning into the mechanismsBayesian mechanisms, Reinforcement Learning

Approximate Solution ConceptsApproximate Nash Equilibrium, etc.

Budget ConstraintsThese constraints are very common in most problems

Computational ChallengesApproximation algorithms?

Dynamic Mechanisms without MoneyPowerful applications can be modeled here

An Interesting Dynamic Mechanism Design Problem

AMALGAM

Researchers and Grad Students (India)

Researchers and Grad Students (USA)

Algorithms based onMAchine Learning,GAme Theory, andMechanism design

E-Commerce Lab, CSA, IISc28

Questions and Answers …

Thank You …