MATH 486: Mathematical Theory of Games is a 3-credit game theory course offered at Penn State. I have had the pleasure to teach, contribute to, and support this course throughout my time as a graduate student, and I have developed this landing page to describe the course in detail.

Content Description

The description you will find on the University Bulletin explains MATH 486 as follows:

Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.

In the Syllabus, students will find:

Game Theory is a wide ranging subject with many applications. We will focus on two main areas: non-cooperative game theory and evolutionary game theory. In our study of non-cooperative game theory we will motivate concepts and ideas with basic applications, develop the abstract mathematical theory from these motivating examples, and then apply and extend the theory to variety of examples. As we examine real applications we will remain mindful of the limitations of the theory.

Course Format

The following link is to a Sample Syllabus, the one used when I taught the course in Summer 2024.

As a three-credit course, there are three 50-minute lectures each week (or equivalent in recorded lectures). For the summer, the course is usually taught asynchronous, remote. Otherwise, the course is synchronous and in-person.

In terms of assessment when I taught the course, two take-home exams (midterm and final) were given outside of class time throughout the semester. Examinations were made available on Canvas and submitted through GradeScope.

Typical assignments include a weekly Homework Assignment, Quiz, and Reflection Assignment.

Course Materials

Textbook

The required textbook for MATH 486 is Game Theory in Action, by Steve Schecter and Herbert Gintis, published by Princeton University Press, 2016.

Lectures

Linked are lecture notes for the course originally written by Christopher Griffin.

My Contribution

I have only taught MATH 486 as a principal instructor in Summer 2024 (one section). But I have TA’d and graded for the course three other times.

My goal as an instructor for MATH 486 was to make sure all of my students felt rewarded by the lectures, assignments, and feedback offered by the course. There are many opportunities to reflect, ask questions, and receive responses through assignments and our Piazza forum. Moreover, I wish for students to learn how to connect game theoretic concepts defined and studied in the course to real life. Students often share that they most enjoy the course content when it teaches them something about a situation they have encountered before.

I must thank Russ deForest for his support in getting me involved in MATH 486, as well as for developing most of the lectures and assignments before I arrived.

I am very grateful for all of the opportunities teaching this course has brought me, and I appreciate all of the kind feedback given to me by previous students.

Bulletin Information

MATH 486 Mathematical Theory of Games is a 3 credit course. This course covers several major classes of models and methods for analyzing multi-party strategic interactions, i.e. games. Specific topics include extensive and strategic form games, continuous games, cooperative games, strictly competitive games, repeated games and adaptive learning, and evolutionary models. The effects on outcomes of information, communication, and other modeling assumptions are discussed. Real-world examples drawn from economics, biology, anthropology, management and everyday life are discussed in detail. When appropriate, computer algebra systems are incorporated in the course. The course typically meets during either two 75-minute periods each week or three 50-minute periods each week. Evaluation methods may vary by instructor, but will typically include a combination of examinations, quizzes, homework, and projects.

Enforced prerequisites upon enrollment are only MATH 220. This course satisfies the Bachelor of Arts Quantification requirement.