  # 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
Syllabus:
Unit NoTopics
1

Introduction

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

2

Dominant Strategy Equilibrium

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

3

Pure Strategy Nash Equilibrium

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

4

Two Player Zerosum 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 simultaneousmoves. Examples

5

Bayesian Games

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

6

Mechanism Design

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

7

Cooperative Game Theory

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

Text Books:
Name :
An Introduction to Game Theory
Author:
Martin Osborne
Publication:
Oxford University Press
Name :
Essentials of Game Theory and Mechanism Design
Author:
Y. Narahari
Publication:
IISc Press
Reference Books:
Name:
Fun and Games : A Text On Game Theory
Author:
Ken Binmore
Publication:
D. C. Heath & Company, 1992.
Syllabus PDF:
AttachmentSize Sem 5 CBA-Game Theory.pdf275.12 KB
branch:
CBA
Course:
2018
Stream:
B.Tech