# Introduction to Game Theory and Mechanism Design

By Prof. Swaprava Nath   |   IIT Bombay
Learners enrolled: 1433
This course is an introduction to game theory and mechanism design. The goal is to equip students with a general purpose tool to analyze strategic behavior in multi-agent interaction. Though primarily a topic of economic flavor, it has significant applications in the decision process of a multi-agent environment like sponsored advertisements, crowdsourcing, social media, internet-based trade, and several settings of social choice and welfare. This course is a backend of such applications and discusses the mathematical details of analyzing and designing strategic interactions.

The evaluation criteria has been updated from the video. The final criteria is mentioned below on this enrollment page

PREREQUISITES : Familiarity with formal mathematical reasoning, probability theory, calculus,basics of computational complexity, and (soft constraint) familiarity with computer programming.

INDUSTRY SUPPORT : Management wing of any company that is interested in mathematical handling of strategic planning will have interest in this course.

CLASS Q&A : We will use Piazza for all class/lecture-related questions and answers. Use this link to enroll yourself: piazza.com/iit_bombay/fall2022/noc22_cs77. The access code is noc22_cs77.
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Computer Science and Engineering Credit Points : 3 Level : Postgraduate Start Date : 25 Jul 2022 End Date : 14 Oct 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 29 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Introduction, the game of chess, proof of chess theorem, normal form games
Week 2:Dominance, Nash equilibrium, Maxmin strategies, elimination of dominated strategies, preservation of pure Nash equilibrium (PSNE), matrix games, relation between maxmin and PSNE in matrix games
Week 3:Mixed strategies, mixed strategy Nash equilibrium (MSNE), finding MSNE, MSNE characterization theorem, algorithm to find MSNE
Week 4:Correlated equilibrium (CE), computing CE, extensive form games, subgame perfection, limitations of subgame perfect Nash equilibrium
Week 5:Imperfect information extensive form games (IIEFG), strategies in IIEFGs, equivalence of strategies in IIEFGs, perfect recall
Week 6:Equilibrium in IIEFG, game theory in practice: P2P file sharing, Bayesian games, strategy and utility in Bayesian games, equilibrium in Bayesian games
Week 7:Introduction to mechanism design, revelation principle, introduction and proof of Arrow’s impossibility result, introduction to social choice setup
Week 1:Introduction and proof of Gibbard-Satterthwaite theorem, domain restriction, median voter theorem
Week 9:Task sharing domain, uniform rule, mechanism design with transfers, examples of quasi-linear preferences, Pareto optimality and Groves payments
Week 10:Introduction to VCG mechanism, VCG in Combinatorial allocations, applications to Internet advertising, slot allocation and payments in position auctions, pros and cons of VCG mechanism
Week 11:Affine maximizers, single object allocation, Myerson’s lemma, optimal mechanism design
Week 12:Single and multi-agent optimal mechanism design, examples of optimal mechanisms

### Books and references

The following books could be helpful.
1. Game Theory” — Michael Maschler, Eilon Solan, Shmuel Zamir
2. Multiagent Systems” — Y. Shoham and K. Leyton Brown, Cambridge University Press, online copy available
3. Game Theory and Mechanism Design” — Y. Narahari, World Scientific and IISc Press – Indian edition available

### Prof. Swaprava Nath

IIT Bombay
Swaprava is an Assistant Professor at the Department of Computer Science and Engineering, IIT Bombay. Before this, he was a faculty member at the Dept. of CSE, IIT Kanpur. Even earlier, he held postdoctoral positions at Carnegie Mellon University and Indian Statistical Institute, New Delhi, and finished his PhD from the Dept. of CSA, IISc Bangalore. His research interest lies at the intersection of economics and computation, which has several applications in social and industrial paradigms (for details, please see his CompEcon group page: https://www.cse.iitb.ac.in/~swaprava/group.html and his research page: https://www.cse.iitb.ac.in/~swaprava/research.html). His work has been published in top AI and multiagent systems conferences, e.g., AAAI, IJCAI, AAMAS, WINE, and also in economics and management venues, e.g., Games and Econ Behavior, Economics Letters, Management Science. Apart from academic positions, Swaprava also has experience in the industry. He has worked at Xerox Research Centre Europe and Cisco Systems India. He has been recipients of Fulbright-Nehru postdoctoral grant, Tata Consultancy Services PhD Fellowship, and the Honorable Mention Award of Yahoo! Key Scientific Challenges Program.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 29 October 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team