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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

Description:

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.

Game Theory

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#Social Sciences #Economics #Game Theory #Nash Equilibrium

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