# Game Theory, Spring Quarter 2005

## Instructor: Thomas S. Ferguson

Office Hours: M 3, Th 2, and by Appointment
Office : MS 6129
e-mail: tom@math.ucla.edu

## Teaching Assistant: Paul Bunn

### Discussion Section: Tu 2, MS 5147

Office Hours: Th 9, Th 11:30, and by Appointment
Office: MS 3903
e-mail: paulbunn@math.ucla.edu

#### Homework Assignments.

Homework will be assigned each class and will be due the following class. Solutions will be posted after the assignments are collected. Late homework will not be graded. Instead, the reader will mark it late after scanning the submission to see it is complete. At the end of the quarter, late homework will be given half credit based on the total score of the graded homework. Please use standard 8 1/2 by 11 paper for your homework. Staples are much preferred to paper clips for holding the pages together.

Friday April 29
Friday May 20

#### Final Exam

Tuesday June 14, 8:00-11:00. To obtain an early report of your grade, leave a stamped, self-addressed postcard with your final exam or in the instructor's mailbox.

#### Course Outline

After the brief overview presented in the Introduction, we will cover
the first four sections of Part I,
the first five sections of Part II,
Appendix 1 on Utility Theory
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.
7. Infinite 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.