MATH 344 - Game Theory

Announcements

We are using a discord forum this term. The TA and I will answer questions there, and post course related announcements. It is open for all students to join.
Lectures have ended. I hope you all had a productive semester.
I will have office hours on zoom this coming monday morning 10:30, at zoom 998.6089.2473.
There will be a review session before the final exam, details TBA. A sample final is posted under exams.

Syllabus

This course covers several topics in Game Theory, an area of Mathematics with multiple applications to Economics, Political Science, Evolutionary Biology, and many other fields. We will encounter important mathematical concepts such as combinatorial methods, fixed point theorems and convexity methods as they are used to prove fundamental results in Game Theory. Topics include:

Combinatorial games (Chess, etc.): extended and strategic forms, Sprague-Grundy theory, games with chance.
Zero-sum games (Poker, etc.): Matrix form, minimax theorem, pure and mixed strategies.
General sum games (Global Thermonuclear War): Nash equilibria, repeated games and evolutionary dynamics, incomplete information.
Coalition games and Shapley values.
Auctions and mechanism design.
Social choice: voting, Arrow's theorem, stable matchings.

Course details

Instructor: Omer Angel. Contact me through discord or by email. Please include "math344" in the subject line.

TA: TBA. If you have any comments for the TA, go through me.

Class times: MWF 12:00 at IRC-4.

Office hours: Office hours will take place after on Monday 10:30 and at Friday 10:00, or by appointment in my office MATX 1210. I am usually available for questions after class.

Online forum: We will use a discord forum this term. You can ask any questions regarding the course there. You are encouraged to ask questions there on lectures, assignments, and any course related topic. You are also encouraged to answer other students’ questions. Significant participation will merit extra credits. Obviously, do not share solutions to assignments (on discord or elsewhere) before the due date.

Textbook: The main book we will follow is Game Theory, Alive, by Karlin and Peres. It is available online freely. Many other books on game theory exist, and may be helpful.

Evaluation

The final mark will be based on:

Additional credits may be given for significant participation in class or on discord.

Missed work: There are no make-up midterms or assignments. Missing a midterm for a valid reason normally results in the weight of the midterm being transferred to the final exam. Personal travel and work conflicts are not considered valid. A student who misses the midterm must submit UBC's self-declaration form within 72 hours of the midterm date or as soon as possible. See the UBC Senate's Academic Concession Policy V-135.