# Mathematics 167

# Game Theory, Spring Quarter 2005

### Time : MWF at 2:00

Place: MS 5147

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
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

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.
Grading will be based on homework, the two midterm examinations
and the final examination. Homework will be worth about half a
midterm, and each midterm will be worth about half the final. Thus,
homework will count about 1/9th of the grade, each midterm about
2/9th, and the final about 4/9th. A student who misses a midterm
exam will be graded on the basis of the homework and the other
exams providing (i) the student has an ironclad excuse (such as
medical emergency), and (ii) the student contacts the instructor on
or before the day of the exam to arrange a conference. A student
who misses the final exam may receive an incomplete (I) grade
providing (i) the student has taken and passed both midterm exams,
(ii) the student has completed the homework at a passing level, (iii)
the student has an ironclad excuse, and (iv) the student contacts the
instructor on or before the day of the final exam to arrange make
arrangements.
The notes for the course are in electronic form in PDF.
To read the notes, you will need the Adobe Acrobat Reader for your
platform. This software can be downloaded free of charge
from the Adobe website at

http://www.adobe.com/products/acrobat/readermain.html.
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.
- Take-Away Games.
- The Game of Nim.
- Graph Games.
- Sums of Games.
- Coin Turning Games.
- Green Hackenbush.

- Part II: Two-person Zero-Sum Games.
- The Strategic Form of a Game.
- Matrix Games. Domination.
- The Principle of Indifference.
- Solving Finite Games.
- The Extensive Form of a Game.
- Recursive and Stochastic Games.
- Infinite Games.

- Part III: Two-Person General-Sum Games.
- Bimatrix Games. Nash Equilibrium.
- The Noncooperative Theory. Safety Levels.
- Models of Duopoly.
- Cooperative Games.

- Part IV: Games in Coalitional Form.
- Many-Person TU Games.
- Imputations and the Core.
- The Shapley Value.
- The Nucleolus.

- Appendix.
- Utility Theory.
- Contraction Maps and Fixed Points.
- Existence of Equilibria in Finite Games.

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.