Mathematics 167, Game Theory, Fall 2000

Course, Time, Classroom

Math 167, M(T)WF 3, MS 5127.

Instructor

Thomas S. Ferguson, MS 7901
e-mail: tom@math.ucla.edu
Office Hours: M 2, Tu 2, Th 3, and by appointment.

Teaching Assistant

Kenneth Tignor, MS 6154
e-mail: ktignor@math.ucla.edu
Office Hours: Th 2-3 in MS 3970 (the student math center) and Th 3-4 in MS 6147.

Text

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

Prerequisite

There are no prerequisites other than the general lower division mathematics courses and Math 115A (linear algebra). However, students with a background in Math 164 (linear programming) and Math 170A (probability) will find the course easier.

Homework

Homework Assignments
Homework will be assigned each class and will be due the following class. 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 x 11 paper for your homework. Staples are much preferred to paper clips for holding the pages together.

Midterm Exams

Friday Oct 20
Friday Nov 17

Final Exam

Tuesday Dec 12, 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.

Hand Calculators

You are encouraged to use calculators when they are useful for solving homework problems. Hand calculators will be permitted for use in the exams.

Grading

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.

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.

Course Outline

The notes for the course are in electronic form in PDF format. To read the notes, you will need the Adobe Acrobat Reader for your platform. This piece of 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, 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. Existence of Equilibria in Finite Games.