# Course Objectives:

The main objective of this course is to introduce the fundamental tools of game theory and a few equilibrium concepts. During this course, we will also look at applications from a variety of disciplines and delve into some of the fascinating mathematics that underlies game theory. This course begins with an introduction into Game Theory. It then introduces strategic and extensive form games, and games with societal aspects to them. Subsequently, we will move onto understanding a few topics/concepts/ideas in mechanism design.

# Course Content

Introduction: Motivation, theory of rational choice, utility functions (3 lectures)

**Strategic form games: **Definition, examples, dominant strategy equilibria, pure strategy Nash equilibrium, mixed strategy Nash equilibrium, existence of Nash equilibrium, computation of Nash equilibria, potential games, two player zero sum games, minimax theorem (15 lectures)

**Extensive form games: **Definition, examples, games of imperfect information, games of incomplete information, repeated games, the folk theorem of average payoffs, Nash equilibrium in repeated games with average payoff (7 lectures)

Cooperative games: Transferable utility games, the core, the Shapley value, Nash bargaining (5 lectures)

Mechanism design: Introduction, social choice functions and mechanisms, incentive compatibility and revelation theorem, the Gibbard-Satterthwaite impossibility theorem, quasilinear mechanisms, Vickrey- Clarke-Groves (VCG) mechanisms, auction, optimal mechanisms and Myerson auction (12 lectures)

# Learning Outcomes:

Upon successful completion of this course, the student will:

1. be able to differentiate between different types of games Identify various equilibria within games
2. gain knowledge about fundamental concepts of non-cooperative and cooperative game theory
3. be able to explain precisely, and apply solution concepts to examples of games
4. be able to apply the mathematical concepts discussed over the duration of the course.

# Text Books:

1. Y. Narahari, â€śGame Theory and Mechanism Design: 4 (IISc Lecture Notes Series),â€ť World Scientific Publishing Co Pvt Ltd, May 07, 2014, ISBN-13: 978-9814525046
2. Anna R. Karlin and Yuval Peres, â€śGame Theory, Alive,â€ť American Mathematical Society, Apr 27, 2017, ISBN-13: 978-1470419820 [Available Online].

# References

1. Siddharth Barman and Y. Narahari, â€śGame Theory Lecture Notesâ€ť Available online at https://lcm.csa.iisc.ernet.in/gametheory
2. Roger B. Myerson, â€śGame Theory: Analysis of Conflict,â€ť Harvard University Press, September 1997, ISBN-13: 978-0674341159.
3. Martin J. Osborne, â€śAn Introduction to Game Theory,â€ť Oxford University Press, 2003, ISBN- 13: 978-0195128956.
4. D. Fudenberg and J. Tirole, â€śGame Theory,â€ť Indian Edition by Ane Books, 2005, ISBN-13: 978-8180520822.

# Past Offerings

• Offered in Aug-Dec, 2022 by Srimanta Bhattacharya