# Game Theory, September 2003

## Aichi University, Japan

#### Course, Time, Classroom

GameTheory, Sep. 1(Mon), 2(Tue), 3(Wed), 5(Fri) 6(Sat), 8(Mon), 9(Tue), 10(Wed)

Two lectures and one problem solving session each day.

#### Instructor

Thomas S. Ferguson
e-mail: tom@math.ucla.edu

#### Text

Game Theory Notes on the web by T. S. Ferguson.

#### Course Outline

The notes for the course are in electronic form in PDF format.

After the brief overview presented in the Introduction, we will cover
the first five sections of Part I,
the first five sections of Part II,
all four sections of Part III, and
all four sections of Part IV.

• Introduction
• Part I: Impartial Combinatorial Games.
1. Take-Away Games.
2. The Game of Nim.
3. Graph Games.
4. Sums of Games.
5. Coin Turning Games.
6. Green Hackenbush.
• Part II: Two-person Zero-Sum Games.
1. The Strategic Form of a Game.
2. Matrix Games. Domination.
3. The Principle of Indifference.
4. Solving Finite Games.
5. The Extensive Form of a Game.
6. Recursive and Stochastic Games.
• Part III: Two-Person General-Sum Games.
1. Bimatrix Games. Nash Equilibrium.
2. The Noncooperative Theory. Safety Levels.
3. Models of Duopoly.
4. Cooperative Games.
• Part IV: Games in Coalitional Form.
1. Many-Person TU Games.
2. Imputations and the Core.
3. The Shapley Value.
4. The Nucleolus.
• Appendix.
1. Utility Theory.
2. Contraction Maps and Fixed Points.
3. Existence of Equilibria in Finite Games.

#### Matrix Game Solver

If you want to find the solution to a matrix game and are willing to type in or paste in the matrix, try the Matrix Game Solver.

## Associated Games.

A few games written in JavaScript to accompany the text may be found in JavaScript Games.