Course Summary

This course will cover the basics of game theory and market design, with a focus on how AI and optimization enables large-scale game solving and markets. We will cover the core ideas behind recent superhuman AIs for games such as Poker. Then, we will discuss how AI and game theory ideas are used in marketplaces such as internet advertising, fair course seat allocation, and energy markets. This is intended to be an advanced MS level and senior undergraduate course for students in Operations Research and Financial Engineering.

Admin stuff

Course Info

• Instructor: Christian Kroer
• Time: Mondays & Wednesdays 10:10-11:25 am
• Location: 313 Fayerweather
• • Professor Office hours:* Wednesday 9-10 am Mudd 314
• • TA Office hours:* Wednesday 4:30-5:45 pm
• Courseworks site: courseworks site

Prerequisites

• Mathematical maturity; ability to follow proofs
• Linear algebra: vector and matrix algebra, eigenvalues
• Calculus: gradients, optimality conditions, Lagrange multipliers
• Optimization: linear programming, mixed-integer programming, some convex optimization (these can potentially be learned along the way). If you are coming from outside IEOR/have not taken classes on these topics, then you should take a look at e.g. this book to get a sense for LP, LP duality, convexity, etc.

Course Structure

The course will be lecture-based, with Christian Kroer giving the lectures. We may also include a few guest lectures from other researchers. At the end of the course there will be a few lectures of project presentations by students.

Readings will be from my textbook draft, which is freely available as a pdf (see link in textbooks section). Supplementary readings will also be suggested, though these are optional.

Students will complete a project, which should be done in groups of 2-4 students (project grading will be done proportional to group size). Special permission is needed to do a 1-person project, and it must be an ambitious research-oriented project.

There will be two tests: a midterm and a final. Both will be during class, one early’ish in the semester, and one in late November/early December. Both tests will be relatively short, since there will only be 1h25m to complete each test.

Grading will be as follows:

• 30% final project write-up
• 15% homework (there will be 4-5 homeworks)
• 20% midterm (midterm will be in class, probably Oct 14th)
• 20% final (final will be in class, probably Nov 25th or Dec 2nd)
• 5% Project proposal
• 5% Project milestone report
• 5% Final project presentation (I may drop presentations depending on how many groups there are)

Bonus credit: Find mistakes in my textbook! Anyone who discovers a mistake in the textbook will be awarded extra credit applied after grade cutoffs are calculated (if a mistake is discovered by more than one person then credit will be split proportionally). If you have improvement suggestions then please share those as well. I will also award extra credit for these if I end up incorporating them. In any case I would love to hear them.

Homework

Homeworks will be posted on courseworks.

Homework lateness policy:

• All homeworks due at midnight on stated date
• Everyone gets 3 late days
• If you are handing in late, you must email the TAs and me to say that you are using a late day. Include in the email how many you have used.

Course Content

Outline

A rough outline is as follows (this is grouped by topic, the presentation ordering will be different):

• Intro to game theory and market design
• No-regret learning
• Nash equilibrium
  • Zero-sum games, minimax theorem
  • Imperfect-information games and poker AIs
• Stackelberg equilibrium, applications to homeland security and wildlife protection
• Market design and the internet
  • Internet advertising auctions
  • Recommender systems
  • Bias and fairness in machine learning and internet advertising
  • Electricity markets
• Fair Resource Allocation
  • Fair division via competitive equilibria
  • Fair course seat allocation
  • Allocating food to food banks

Textbooks

The primary text will be my book draft. I will also fequently mention complementary reading from the AGT book:

• AI, Games, and Markets draft (CK) by Kroer (free)
• Algorithmic Game Theory (AGT) by Nisan, Roughgarden, Tardos, and Vazirani (it’s free)

Additionally, we may use some sections of the following books. They are also recommended for supplementary reading:

• Handbook of Computational Social Choice (HCSC) by Brandt, Conitzer, Endriss, Lang, & Procaccia (it’s free, password: cam1CSC)
• Multiagent Systems (MS) by Leyton-Brown & Shoham (it’s free)
• Twenty Lectures on Algorithmic Game Theory (TLAGT) by Tim Roughgarden (the individual notes can be found on Tim’s website under the course “Algorithmic Game Theory”)
• Introduction to Online Convex Optimization (Hazan) by Hazan (it’s free)
• A Modern Introduction to Onlinea Learning (Orabona) by Orabona (it’s free)

If you want to practice problem-solving in order to prepare better for the exam, you can find exercises in the following books:

• Algorithmic Game Theory (AGT) by Nisan, Roughgarden, Tardos, and Vazirani (it’s free)
• Networks, Crowds, and Markets by Easley and Kleinberg (I link to a free preprint of the book)
• Game Theory: Analysis of Conflict by Roger Myerson (ebook available through CLIO)

Project

Students will complete a half-semester project on topics related to the course. This project can be applied, theoretical, or a mixture. Students are encouraged to formulate their own project proposals. That said, I will also provide some candidate project topics on courseworks.

Project rules:

• Teams should have 2-4 students. Solo projects require instructor permission and an ambitious scope.
• A one-page project proposal is due November 6th
• A 2-page progress report is due November 22nd
• A 5-10 page whitepaper, formatted as a NeurIPS conference paper, is due December 22nd
• Each team must make a ~20m presentation of their project

Tentative Schedule

Related Courses

Below is a list of related courses.