Computational Game Theory

Lecture 1: Zero Sum Games and Pure Strategies, saddle point

Chapter 2 of Reference text (3) 

Chapter 6 of Penn State Lecture Notes

Chapter 9 of Reference text (2)

Lecture 2: Zero Sum Games, Mixed Strategies, Equilibria

Chapter 4 of Reference text (3) 

Chapter 6 and 8 of Penn State Lecture Notes

Chapter 5 of Reference text (2)

Online rock, paper, scissors

Lecture 3: Donimant Strategies and Equilibria

Chapter 4, 5 of Reference text (2)

Lecture 4: Example of a set of linear equations in 2D, graphical solutions.
Introduction to linear programming (LP), LP duality, Statement of the strong duality theorem, Weak duality theorem and its proof, Polyhedral set, Farkas Lemma and its proof.

Introduction to Linear Optimization

Chapter 3 and 4 of Reference text (4)

Lecture 5: Representation of Polyhedral set, completely mixed games, Minmax theorem

Introduction to Linear Optimization

Chapter 9 of Reference text (2)

Chapter 3 and 4 of Reference text (4)

Lecture 6: Utility Theory

Chapter 2 of Reference text (5)

Chapter 8 of Reference text (2)

Lecture 7: Non-cooperative games: Nash equilibrium

Chapter 10 of Reference text (2)

Lecture 8: Non-cooperative games: Existence of Nash equilibrium, Kakutani's fixed point theorem

Chapter 10 of Reference text (2)

Lecture 9: Sperner's Lemma, Brouwer's fixed point theorem, and existence of Nash equilibria

Chapter 10 of Reference text (2)

Chapter 6.2 and 6.3 of Reference text (4)

Lecture 10: Linear Complementary Problem (LCP): Introduction

Lecture 11: LCP and Computing Nash Equilibrium 

Chapter 1.1 and 1.4 of Reference text (6)

Chapter 11 of Reference text (2)

Lecture 12: Complexity of Computing Nash Equilibrium

Chapter 12 of Reference text (2)

Chapter 2 of Reference text (1)

Daskalakis, Goldberg, and Papadimitriou 2009

Lipton, Markakis, and Mehta 2003

Lecture 13: Bayesian Games, 

Cooperative Games: Introduction, Diving a dollar game

Chapter 13 of Reference text (2)

Chapter 6.3 of Reference text (7) 

Chapter 27 of Reference text (2)

Chapter 12 of Reference text (7) 

Lecture 14: Cooperative Games: Solution Concepts: Stable sets, exsistence, uniqueness

Chapter 30 of Reference text (2)

Lecture 15: Cooperative Games: Solution Concepts: Core, LP formulation, Exsistance of Core, Bondareva-Shapley Theorem,  Banzhaf index

Chapter 28 of Reference text (2)

Lecture 16: Cooperative Games: Solution Concepts: Shapley Value

Chapter 29 of Reference text (2)

Lecture 17: Cooperative Games: Least Core, Nucleolus, Bargaining Set. NTU Games: Additively separable, friends based hedonic games

Chapter 30 of Reference text (2)

Chapter 5 of Reference text (8)

Cooperative games with coalition structures

Coalition Formation Games: A Survey by Jana Hajduková

Lecture 18: Introduction to Mechanism Design

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Lecture 25