Transcript Indian Institute of Science

Design of Mechanisms for
Dynamic Environments
November 12, 2010
Y. NARAHARI
http://lcm.csa.iisc.ernet.in/hari
INDO – US WORKSHOP ON
MACHINE LEARNING, GAME THEORY, AND OPTIMIZATION
Computer Science and Automation
Indian Institute of Science, Bangalore
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E-Commerce Lab, CSA, IISc
OUTLINE
Static Mechanism Design and Our Work
Dynamic Mechanisms and Current Art
Outlook for Future and
Opportunities for Collaboration
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E-Commerce Lab, CSA, IISc
Mechanism Design
Design of games / reverse engineering of games
Game Engineering
Induces a game among rational and intelligent
players such that in some equilibrium of the game,
a desired social choice function is implemented
William Vickrey
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Leonid Hurwicz
Eric Maskin
Roger Myerson
E-Commerce Lab, CSA, IISc
A Mechanism Without Money
Fair Division of a Cake
Mother
Social Planner
Mechanism Designer
Kid 1
Rational and
Intelligent
Kid 2
Rational and
Intelligent
A Mechanism with a lot of Money
Mumbai
Indians
1
Kolkata
Knight Riders
2
Bangalore
RoyalChallengers
3
Punjab Lions
Sachin Tendulkar
4
IPL Franchisees
IPL CRICKET AUCTION
The Famous Corus Auction (31-1-2007)
Tata Steel
US$ 12.04 Billion
CSN
(Brazilian
Company)
Problem 1: Procurement Auctions
SUPPLIER 1
SUPPLIER 2
Buyer
SUPPLIER n
Supply (cost) Curves
T.S. Chandrasekhar, Y. Narahari, Charlie Rosa, Pankaj Dayama,
Datta Kulkarni, Jeffrey Tew. IEEE T-ASE, 2006
PROBLEM 2: Sponsored Search Auction
Advertisers
1
2
n
CPC
D. Garg and Y. Narahari. IEEE T-ASE, 2009
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E-Commerce Lab, CSA, IISc
Problem 3: Carbon Credit Allocator
Division 1
cost
No of Carbon Credits
CCA
Carbon Credit
Allocator
cost
.
Division n
No of Carbon Credits
A. Radhika, Y. Narahari, D. Bagchi, P. Suresh, S.V. Subrahmanya.
Journal of IISc, 2010
Problem 4: Crowdsourcing
Determine winner
Read
Post
Problem
Respon
d
Review
Problem
Verify Task
Receive
Bids
Assign
Complete
Confirm Payment
Pay
Resolve
any
Dispute
Ask
Read
Place Bids
Complete Task
Karthik Subbian, Ramakrishnan Kannan, Y. Narahari, IEEE APSEC, 2007
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E-Commerce Lab, CSA, IISc
PROPERTIES OF SOCIAL CHOICE FUNCTIONS
DSIC (Dominant Strategy
Incentive Compatibility)
Reporting Truth is always good
AE (Allocative Efficiency)
Allocate items to those who
value them most
Non-Dictatorship
No single agent is favoured all
the time
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BIC (Bayesian Nash
Incentive Compatibility)
Reporting truth is good whenever
others also report truth
BB (Budget Balance)
Payments balance receipts and
No losses are incurred
Individual Rationality
Players participate voluntarily
since they do not incur losses
E-Commerce Lab, CSA, IISc
POSSIBILITIES AND IMPOSSIBILITIES - 1
Gibbard-Satterthwaite Theorem
When the preference structure is rich,
a social choice function is DSIC iff it is dictatorial
Groves Theorem
In the quasi-linear environment, there exist social
choice functions which are both AE and DSIC
The dAGVA Mechanism
In the quasi-linear environment, there exist social
choice functions which are AE, BB, and BIC
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E-Commerce Lab, CSA, IISc
POSSIBILITIES AND IMPOSSIBILITIES -2
Green- Laffont Theorem
When the preference structure is rich, a social
choice function cannot be DSIC and BB and AE
Myerson-Satterthwaite Theorem
In the quasi-linear environment, there cannot exist
a social choice function that is
BIC and BB and AE and IR
Myerson’s Optimal Mechanisms
Optimal mechanisms are possible subject to
IIR and BIC (sometimes even DSIC)
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E-Commerce Lab, CSA, IISc
WBB
SBB
EPE
dAGVA
DSIC
BIC
MECHANISM
DESIGN SPACE
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MYERSON
GROVES
AE
CBOPT
SSAOPT
VDOPT
IR
E-Commerce Lab, CSA, IISc
Our work is summarized in
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E-Commerce Lab, CSA, IISc
Limitations of Classical Mechanisms
Do not model the repeated/sequential nature of
decision making
Do not model dynamic evolution of types
Do not model dynamic populations
Do not model any learning by the agents
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E-Commerce Lab, CSA, IISc
Dynamic Mechanisms
Types could be dynamic
(Dynamic type mechanisms)
Population could be dynamic
(Online mechanisms)
Can capture sequential decision making
and learning
Criterion could be social welfare or
revenue maximization or cost minimization
Could be with money or without money
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E-Commerce Lab, CSA, IISc
Dynamic (Type) Mechanisms
Dirk Bergemann and Juuso Valimaki
The Dynamic Pivot Mechanism, Econometrica, 2010
Susan Athey and Ilya Segal
An Efficient Dynamic Mechanism, Tech Report 2007
Ruggiero Cavallo, Efficiency and Redistribution in
Dynamic Mechanism Design, EC 2008
Alessandro Pavan, Ilya Segal, and Jusso Toikka
Dynamic Mechanism Design: Incentive Compatibility,
Profit Maximization, Information Disclosure, 2009
Ruggiero Cavallo, David Parkes, and Satinder Singh
Efficient Mechanisms with Dynamic Populations and Types,
July 2009
Topics in Game Theory Team, IISc
Dynamic Mechanisms for Sponsored Search Auction, Ongoing
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E-Commerce Lab, CSA, IISc
Multi-Armed Bandit Mechanisms
Avrim Blum and Y. Mansour. Learning, Regret Minimization,
And Equilibria. In: Algorithmic Game Theory, 2007
Nikhil Devanur and Sham Kakade
The Price of Truthfulness for Pay-per-click Auctions, EC 2009
Moshe Babaioff, Yogeshwar Sharma, Aleksandrs Slivkins
Characterizing Truthful MAB Mechanisms, EC 2009
Akash Das Sharma, Sujit Gujar, Y. Narahari
Truthful MAB Mechanisms for Multi-slot Auctions, 2010
Sai Ming Li, Mohammad Mahdian, R. Preston McAfee
Value of Learning in Sponsored Search Auctions, WINE 2010
Sham Kakade, Ilan Lobel, and Hamid Nazerzadeh
An Optimal Mechanism for Multi-armed Bandit Problems, 2010
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E-Commerce Lab, CSA, IISc
Online Mechanisms
David Parkes and Satinder Singh
An MDP-Based Approach to Online Mechanism Design, NIPS’03
David Parkes, Online Mechanism Design
Book Chapter: Algorthmic Game Theory, 2007
Alex Gershkov and Benny Moldovanu
Dynamic Revenue Maximization with Heterogeneous Objects
American Economic Journal, 2008
Mallesh Pai and Rakesh Vohra
Optimal 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 Assignment
Without Money, AAAI 2010
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E-Commerce Lab, CSA, IISc
Problem 1: Procurement Auctions
SUPPLIER 1
SUPPLIER 2
Buyer
SUPPLIER n
Supply (cost) Curves
Budget Constraints, Lead Time Constraints, Learning by Suppliers,
Learning by Buyer, Logistics constraints, Combinatorial Auctions,
Cost Minimization, Multiple Attributes
PROBLEM 2: Sponsored Search Auction
Advertisers
1
2
n
CPC
Budget Constraints, Learning by the Search Engine, Learning by the
Advertisers, Optimal Auctions
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E-Commerce Lab, CSA, IISc
Problem 3: Carbon Credit Allocator
Division 1
cost
No of Carbon Credits
CCA
Carbon Credit
Allocator
cost
.
Division n
No of Carbon Credits
Budget constraints, Learning by the Allocator
Problem 4: Crowdsourcing
Determine winner
Read
Post
Problem
Respon
d
Review
Problem
Verify Task
Receive
Bids
Assign
Complete
Confirm Payment
Pay
Resolve
any
Dispute
Ask
Read
Place Bids
Complete Task
Ticket Allocation, Group Ticket Allocation, Learning, Dynamic Population
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E-Commerce Lab, CSA, IISc
Problem 5: Amazon Mechanical Turk
A Plea to Amazon: Fix Mechanical Turk! Noam Nisan’s Blog – October 21, 2010
Dynamic Mechanisms: Some Generic Issues
Possibility and Impossibility Results
For example: Does Green-Laffont Theorem hold for
dynamic mechanisms?
Incorporate learning into the mechanisms
Bayesian mechanisms, Reinforcement Learning
Approximate Solution Concepts
Approximate Nash Equilibrium, etc.
Budget Constraints
These constraints are very common in most problems
Dynamic Mechanisms without Money
Powerful applications can be modeled here
Computational Challenges
Approximation algorithms?
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E-Commerce Lab, CSA, IISc
An Interesting Dynamic Mechanism
Design Problem
AMALGAM
Algorithms based on
MAchine Learning,
GAme Theory, and
Mechanism design
Researchers and
Grad Students
(India)
Researchers and
Grad Students
(USA)
Questions and Answers …
Thank You …
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E-Commerce Lab, CSA, IISc