COURSE OUTLINE: Game theory models conflict and cooperation between decision-makers who are assumed to be rational. It has applications in multiple disciplines and areas. The aim of this course is to introduce the following topics at a basic level: combinatorial games, zero-sum games, non-zero sum games and cooperative games. Learning outcomes for the course: At the end of the course, the student should be able to • Model and analyse conflicting situations using game theory.
Overview
Syllabus
Introduction-Game Theory.
Lecture 1 : Combinatorial Games: Introduction and examples.
Lecture 2 : Combinatorial Games: N and P positions.
Lecture 3 : Combinatorial Games: Zermelo’s Theorem.
Lecture 4 : Combinatorial Games: The game of Hex.
Lecture 5 : Combinatorial Games: Nim games.
Lecture 6: Combinatorial Games: Sprague-Grundy Theorem - I.
Lecture 7: Combinatorial Games: Sprague-Grundy Theorem - II.
Lecture 8: Combinatorial Games: Sprague-Grundy Theorem - III.
Lecture 9: Combinatorial Games: The Sylver Coinage Game.
Lecture 10: Zero-Sum Games: Introduction and examples.
Lecture 11 : Zero-Sum Games: Saddle Point Equilibria & the Minimax Theorem.
Lecture 12 : Zero-Sum Games: Mixed Strategies.
Lecture 13 : Zero-Sum Games: Existence of Saddle Point Equilibria.
Lecture 14 : Zero-Sum Games: Proof of the Minimax Theorem.
Lecture 15 : Zero-Sum Games: Properties of Saddle Point Equilibria.
Lecture 16 : Zero-Sum Games: Computing Saddle Point Equilibria.
Lecture 17 : Zero-Sum Games: Matrix Game Properties.
Lecture 18 : Non-Zero-Sum Games: Introduction and Examples.
Lecture 19 : Non-Zero-Sum Games: Existence of Nash Equilibrium Part I.
Lecture 20 : Non-Zero-Sum Games: Existence of Nash Equilibrium Part II.
Lecture 21 : Iterated elimination of strictly dominated strategies.
Lecture 22 : Lemke-Howson Algorithm I.
Lecture 23 : Lemke-Howson Algorithm II.
Lecture 24 : Lemke-Howson Algorithm III.
Lecture 25 : Evolutionary Stable Strategies -I.
Lecture 26 : Evolutionarily Stable Strategies - II.
Lecture 27 : Evolutionarily Stable Strategies - III.
Lecture 28 : Fictitious Play.
Lecture 29 : Brown-Von Neumann-Nash Dynamics.
Lecture 30 : Potential Games.
Lecture 31 : Cooperative Games: Correlated Equilibria.
Lecture 32 : Cooperative Games: The Nash Bargaining Problem I.
Lecture 33 : Cooperative Games: The Nash Bargaining Problem II.
Lecture 34 : Cooperative Games: The Nash Bargaining Problem III.
Lecture 35 : Cooperative Games: Transferable Utility Games.
Lecture 36 : Cooperative Games: The Core.
Lecture 37 : Cooperative Games: Characterization of Games with non-empty Core.
Lecture 38 : Cooperative Games: Shapley Value.
Lecture 39 : Cooperative Games: The Nucleolus.
Lecture 40 : The Matching Problem.
Taught by
IIT Bombay July 2018
