Term: Summer 2021, May 24 – June 11.
Course meets: Virtually, Mon-Tue-Thu-Fri, 8:45-noon (Pacific time). The private Zoom link was sent by e-mail, and is also available on the course Sakai page.
Office Hours: By appointment, usually at 1:30pm.
People make decisions everyday — small ones such as what to eat or wear, to large ones such as which job to take or whether to buy a house. Groups of people also make decisions, such as which president to elect, or what policies to adopt, what business strategies to pursue. Mathematics has much to offer the decision-maker — both in the analysis of strategies and suggestions for a course of action.
In this course, we will focus on the modeling of individual and group decisions using mathematical techniques from “game theory”, the area of mathematics that was pioneered in the 1950’s by John Nash and others, but now has applications to a wide variety of disciplines: economics, biology, computer science.
Topics will include: basic concepts of game theory and social choice theory, representations of games, Nash equilibria, utility theory, non-cooperative games, cooperative games, voting games, paradoxes, Arrow’s impossibility theorem, Shapley value, power indices, “fair division” problems, and applications.
Math 55 (or some experience with discrete math) is recommended, but not required.
- Phil Straffin, Game Theory and Strategy.
- Alan Taylor and Allison Pacelli, Mathematics and Politics.
E-books are available through the Claremont Colleges Library at these links: Straffin, Taylor-Pacelli.
As a 3-week summer course, there will be daily homework, which in the latter part of the course will include time to work on final projects. There will also be an exam at the beginning of week 3.
Homeworks will be graded based on clarity of ideas and communication. You’ll note that Straffin has all answers at the back of the text, but these are rather minimal. (On the Honor Code, do NOT look at them until AFTER you have attempted each problem.) You’ll need to explain how you arrived at your answers to get full credit. Good communication is important in this class; be sure to read my Guidelines for Good Mathematical Writing.
All homework will be submitted through Gradescope. Access this through the Sakai course page. On the left tab, you’ll see a link for Gradescope. You will need to upload by scanning your homework, and tagging which portion is associated with specific problems. Here is some guidance on how to do that: https://www.gradescope.com/get_started#student-submission.
There will be one take-home exam due at the start of Week 3.
There will be a final project involving a critical analysis of the relationship of the mathematical methods of game theory to contemporary society. This will be a group project (2 to 3 students). You will create a video presentation of up to 10 minutes.
Homework, Exam, Final Project are each worth 25%, with highest component worth 25%. The grader for the course is Allen Wu.