# Learning Objectives

The main objective of this course is to introduce the fundamental tools of game theory, a few equilibrium concepts, apart from numerous exercises.

# Learning Outcome

Upon successful completion of this course, students are expected to:

• Differentiate between different types of games
• Identify various equilibria within games
• Gain knowledge about fundamental concepts of non-cooperative and cooperative game theory
• Explain precisely, and apply solution concepts to examples of games
• Retain and apply the mathematical concepts discussed over the duration of the course.

# 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, potential games, games with infinite strategy space, zero sum games, minimax theorem, Braess paradox, price of anarchy. [7 lectures]

Extensive form games: definition, examples, games of imperfect information, games of incomplete information, repeated games, the folk theorem of average payoffs. [6 lectures]

Designing games and mechanisms: Fair division, stable matching and allocation, auctions, truthful auctions in win/lose settings, Vickrey-Clarke-Groves mechanism, scoring rules, matching markets [10 lectures]

Cooperative games: Transferable utility games, the core, the Shapley value, Nash bargaining [8 lectures]

Social choice and voting: Voting and ranking mechanism, Arrowâ€Ÿs Impossibility Theorem, The Gibbard-Satterthwaite Theorem, desirable properties of voting and ranking [8 lectures]

# Textbooks

1. Anna R. Karlin and Yuval Peres, Game Theory, Alive, American Mathematical Society, Apr 27, 2017, ISBN-13: 978-1470419820 [Available Online].

# References

1. Siddharth Barman and Y. Narahari, Game Theory Lecture Notes [Available online at http://lcm.csa.iisc.ernet.in/gametheory]

2. Roger B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, September 1997, ISBN-13: 978-0674341159.

3. Martin J. Osborne, An Introduction to Game Theory, Oxford University Press, 2003, ISBN-13: 978-0195128956.

4. D. Fudenberg and J. Tirole, Game Theory, Indian Edition by Ane Books, 2005, ISBN-13: 978-8180520822.

# Past Offerings

• Offered in July-Dec, 2018 by Albert