Math 167: Mathematical Game Theory

Winter 2017

Material: in this course we will try to understand the mathematical theory behind games. In a nutshell, during the lectures we will consider combinatorial games, zero-sum games, general sum games, the min-max theorem of von Neumann, the notion of Nash equilibria, etc. During the last 2-3 weeks we will consider some differential games as well.

Instructor: Alpár R. Mészáros, MS 5230 (check the e-mail address on my webpage or on CCLE)

Schedule of classes: MWF - 8-8h50AM

Office hours: M-W, 9h00-10h30AM

Location: MS 5127

TA: Brent Woodhouse, MS 6153

Discussion: Thursday, 8-8h50AM (same room as for the lecture)

TA's office hours: TBA

Texts: the main text is the lectures notes of Yuval Peres on game theory. This also has a format of a book and the draft of it can be freely accessed at his webpage (see here). The book will be published in 2017 by AMS as A. R. Karlin, Y. Peres - Game Theory, Alive.
Another text that we will use, is T. S. Ferguson - Game theory, 2014. This can be also accessed freely here.

Requisites: we will rely a lot on linear algebra, thus a course like Math 115A is recommended. We will need some basic notions from probability and ODEs, but these will be recalled when needed.

Homework problems will be assigned weekly (i.e. 10 sets) and collected at the beginning of the Friday lecture (if Friday is a holiday the collection date is next Monday at the beginning of the lecture). The purpose of the homework exercises is to deepen the notions and the concepts learned during the lectures. A second purpose is to gain experience with computation techniques and see as many examples as possible. Please note that late- or no homework papers will be graded as zero, but the two lowest homework scores will be dropped in the computation of your final grade (see 'Grading' section below). The homework sheets will appear on this webpage, approximately 1 week before their deadline. There is a possibility to work in groups on the homework problems. In this case, everybody from the group has to submit his/her own homework paper and should write the names of the other students from his/her group on the top of the papers.

Exams: there will be two midterms (see the precise dates below) and a written final exam at the end. No make-up exams will be provided, a missed exam is graded as zero. You must take the final in order to pass the class!

Grading: the final score is calculated as follows. I will chose the scheme which gives you higher final score:
10% HG + 40% ((MG1+MG2)/2) + 50% FG,
or
10% HG + 25% max(MG1;MG2) + 65% FG, where

HG = the average of the homework grades, except the two lowest ones

MG1, MG2 = the two midterm grades

FG = the grade of the final exam

Date of the first midterm: Friday, February 3, 2017, time and place: during the lecture, in the same room.

Date of the second midterm: Friday, March 3, 2017, time and place: during the lecture, in the same room.

Date of the final exam: Monday, March 20, 2017, 8-11AM, place: same room as for the lectures;

Regrading for the homework papers, the midterms and the final should be requested within 2 weeks of their due date and exam dates respectively. Any requests after this period will be not taken into consideration.

Homework sheets