2CSE50E6: Game Theory

Learning Outcomes: 
Upon Completion of the course, the students will be able to
Understand the importance of competitive and cooperative factors in a variety of decision problems
Learn how to structure and analyse these problems from a quantitative perspective
Learn to understand why there exist a special theory on strategic interaction and learn the basic notions of game theory
Learn to solve non-cooperative games with different concepts (dominance, maximin, Nash equilibrium)
Learn to formalize and to solve games with a sequential structure
Learn to understand the role of information in strategic interaction and learn to analyze games with imperfect and incomplete information
Learn to understand the difference between non-cooperative and cooperative games; learn solution concepts for cooperative games; learn to understand and solve evolutionary games
Unit NoTopics

What is Game Theory? Definition of Games. Actions, Strategies, Preferences, Payoffs. Examples; Strategic Form Games - Strategic form games and examples: Prisoner's Dilemma, Bach or Stravinsky, Matching Pennies, Tragedy of Commons, Braess Paradox

Dominant Strategy Equilibrium

Strongly dominant strategies, weakly dominant strategies, dominant strategy equilibrium; Examples of Prisoner‟s Dilemma and Vickrey Auction

Pure Strategy Nash Equilibrium

Best response strategies; Notion of pure strategy Nash equilibrium. Examples of Nash Equilibrium. Examples of Nash Equilibrium in popular games. Symmetric Games and Symmetric Equilibria; Mixed Strategy Nash Equilibrium- Randomization of Actions, Mixed strategy Nash equilibrium, Necessary and sufficient conditions for a Nash equilibrium. Examples of mixed strategy Nash equilibrium. Computing mixed strategy Nash equilibria. Related algorithmic issues

Two Player Zero sum Games (Matrix Games)

Max-minimization and Minmaximization. Saddle points. Nash equilibrium in matrix games. Mini-max theorem. Solution via linear programming. Examples; Extensive games with Perfect Information-Extensive games, Strategies and outcomes, Nash equilibrium, Subgame perfect equilibrium, finding subgame perfect equilibria using backward induction. Allowing for simultaneous moves. Examples

Bayesian Games

Motivational Examples. Definition of a Bayesian Game and Bayesian Nash Equilibrium and examples

Mechanism Design

Social choice functions. Direct and indirect mechanisms. Notion of incentive compatibility. Revelation theorem. Properties of social choice functions. Gibbard Satterthwaite theorem. Quasi-linear utilities. Vickrey auction. Clarke mechanisms. Groves mechanisms. Examples of VCG (Vickrey-Clarke- Groves) mechanisms. Different types of auctions. Revenue equivalence theorem

Cooperative Game Theory

Correlated strategies and correlated equilibrium. The two person Nash bargaining problem and its solution with examples. Games in characteristic form and examples. . The Core of a characteristic form game. Shapley value and its implications. Examples

Text Books: 
Name : 
An Introduction to Game Theory
Martin Osborne
Oxford University Press, 2003.
Name : 
Essentials of Game Theory and Mechanism Design
Y. Narahari
IISc Press, 2011
Reference Books: 
Game Theory and Strategy
Jr. Phiip D. Straffin
The Mathematical Association of America, January 1993
A Text On Game Theory
Ken Binmore
D. C. Heath & Company, 1992
Syllabus PDF: 
PDF icon 5th Game Theory.pdf239.46 KB