These course notes cover topics in mathematics, game theory, and microeconomic theory (generally relating to competitive demand and competitive equilibrium). The notes are pitched at an advanced undergraduate or first-year graduate level.

All of my notes are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License: read and distribute but don’t copy for commercial use.

I’m responsible for all errors. I find errors all the time; apologies for that, but you have been warned. My intention is to keep these notes updated, correcting errors as I find them. That is one of the attractions for me of posting these notes to the web rather than creating a conventional book.

My notes contain some, but not many, citations. When in doubt, assume that I first learned the material from someone else. Here are a few of the people to whom I owe an intellectual debt.

My PhD committee consisted of Andreu Mas-Colell (Chair), Eric Maskin, and Vijay Krishna. Andreu and Eric were also on my orals committee.

Math. I took my first analysis course at Yale from Shizuo Kakutani, who used Rudin (Principles of Analysis). The grade distribution for the first midterm in that course was along the lines, one person got 72, one person got 12, and the rest of the class, perhaps 20 people, got nothing. My notes here have also been heavily influenced by Royden (Real Analysis), Munkres (Topology), and Enderton (A Mathematical Introduction to Logic, and also Elements of Set Theory).

Game Theory. My first sustained exposure to game theory was in my first semester of graduate school, fall 1983, from David Kreps (when he spent a semester at Harvard). My first full course in game theory was from Eric Maskin, when he was still at MIT. From graduate school, I also owe a big debt to Dilip Abreu, Adam Brandenburger, Drew Fudenberg, and Vijay Krishna.

Microeconomic Theory. My first exposure to graduate level microeconomic theory was when I was an undergraduate at Yale. The course was taught by Katsuhito Iwai and used Varian (Microeconomic Analysis, first edition). I also owe a debt to everyone mentioned under game theory. And to Andreu, of course, Herbert Scarf (I took his year-long grad course at Yale, when I was an undergrad), and Mike Winston, among others. I should also mention my introductory microeconomics class, taught by Raymond Powell. Powell’s course took theory more seriously than is standard, which was an eye opener for me and inspired me to take additional economics courses.

I’d like to thank the grad students who, over the years, have helped with these notes in various ways. These include Carmen Astorne-Figari, Juan Carlos Carbajal, Meichen Chen, Sunha Myong, Jiemai Wu, and Lintao Ye.

I need to add people to this list, but it’s a start. These notes are a work in progress and many, many people have helped make them better.