Design of Mechanisms for Dynamic Environments

1. 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 E-Commerce Lab, CSA, IISc

2. OUTLINE Static Mechanism Design and Our Work Dynamic Mechanisms and Current Art Outlook for Future and Opportunities for Collaboration E-Commerce Lab, CSA, IISc

3. 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 Eric Maskin Leonid Hurwicz Roger Myerson William Vickrey 3 E-Commerce Lab, CSA, IISc

4. A Mechanism Without MoneyFair Division of a Cake Mother Social Planner Mechanism Designer Kid 1 Rational and Intelligent Kid 2 Rational and Intelligent

5. A Mechanism with a lot of Money Mumbai Indians 1 Kolkata Knight Riders 2 Bangalore RoyalChallengers 3 Punjab Lions 4 Sachin Tendulkar IPL Franchisees IPL CRICKET AUCTION

6. The Famous Corus Auction (31-1-2007) Tata Steel CSN (Brazilian Company) US$ 12.04 Billion

7. Problem 1: Procurement Auctions SUPPLIER 1 SUPPLIER 2 Buyer SUPPLIER n Supply (cost) Curves T.S. Chandrasekhar, Y. Narahari, Charlie Rosa, PankajDayama, DattaKulkarni, Jeffrey Tew. IEEE T-ASE, 2006

8. PROBLEM 2: Sponsored Search Auction Advertisers CPC D. Garg and Y. Narahari. IEEE T-ASE, 2009 E-Commerce Lab, CSA, IISc

9. Problem 3: Carbon Credit Allocator Division 1 cost CCA No of Carbon Credits Carbon Credit Allocator cost Division n . No of Carbon Credits • Radhika, Y. Narahari, D. Bagchi, P. Suresh, S.V. Subrahmanya. Journal of IISc, 2010

10. Determine winner Read Respond Verify Task Confirm Payment Post Problem Review Problem Receive Bids Assign Complete Pay Resolve any Dispute Ask Read Place Bids Complete Task Problem 4: Crowdsourcing KarthikSubbian, RamakrishnanKannan, Y. Narahari, IEEE APSEC, 2007 10 E-Commerce Lab, CSA, IISc

11. PROPERTIES OF SOCIAL CHOICE FUNCTIONS BIC (Bayesian Nash Incentive Compatibility) Reporting truth is good whenever others also report truth DSIC (Dominant Strategy Incentive Compatibility) Reporting Truth is always good AE (Allocative Efficiency) Allocate items to those who value them most BB (Budget Balance) Payments balance receipts and No losses are incurred Non-Dictatorship No single agent is favoured all the time Individual Rationality Players participate voluntarily since they do not incur losses E-Commerce Lab, CSA, IISc

12. 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 12 E-Commerce Lab, CSA, IISc

13. 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) 13 E-Commerce Lab, CSA, IISc

14. WBB SBB AE EPE dAGVA BIC IR CBOPT DSIC GROVES SSAOPT VDOPT MYERSON MECHANISM DESIGN SPACE 14 E-Commerce Lab, CSA, IISc

15. Our work is summarized in E-Commerce Lab, CSA, IISc

16. 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 16 E-Commerce Lab, CSA, IISc

17. 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 17 E-Commerce Lab, CSA, IISc

18. Dynamic (Type) Mechanisms Dirk Bergemannand JuusoValimaki 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 JussoToikka 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 18 E-Commerce Lab, CSA, IISc

19. 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, AleksandrsSlivkins Characterizing Truthful MAB Mechanisms, EC 2009 Akash Das Sharma, SujitGujar, 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, IlanLobel, and Hamid Nazerzadeh An Optimal Mechanism for Multi-armed Bandit Problems, 2010 19 E-Commerce Lab, CSA, IISc

20. 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 MalleshPai and RakeshVohra Optimal Dynamic Auctions, Kellogg Report, 2008 Florin Constantin and David Parkes, Self-correcting, Sampling-based, Dynamic Multi-unit Auctions, EC 2009 James Jou, SujitGujar, David Parkes, Dynamic Assignment Without Money, AAAI 2010 20 E-Commerce Lab, CSA, IISc

21. 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

22. PROBLEM 2: Sponsored Search Auction Advertisers CPC Budget Constraints, Learning by the Search Engine, Learning by the Advertisers, Optimal Auctions E-Commerce Lab, CSA, IISc

23. Problem 3: Carbon Credit Allocator Division 1 cost CCA No of Carbon Credits Carbon Credit Allocator cost Division n . No of Carbon Credits Budget constraints, Learning by the Allocator

24. Determine winner Read Respond Verify Task Confirm Payment Post Problem Review Problem Receive Bids Assign Complete Pay Resolve any Dispute Ask Read Place Bids Complete Task Problem 4: Crowdsourcing Ticket Allocation, Group Ticket Allocation, Learning, Dynamic Population 24 E-Commerce Lab, CSA, IISc

25. Problem 5: Amazon Mechanical Turk A Plea to Amazon: Fix Mechanical Turk! Noam Nisan’s Blog – October 21, 2010

26. 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? 26 E-Commerce Lab, CSA, IISc

27. An Interesting Dynamic Mechanism Design Problem AMALGAM Algorithms based on MAchine Learning, GAme Theory, and Mechanism design Researchers and Grad Students (USA) Researchers and Grad Students (India)

28. Questions and Answers … Thank You … 28 E-Commerce Lab, CSA, IISc