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 spectrum reallocation. 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 1:10-2:25pm
• Location: 303 Seeley W. Mudd Building
• • Professor Office hours:* Wednesday 2:25-3:30pm Mudd 314
• • TA Office hours:* Tuesday 9-10am Mudd 301
• Courseworks site: courseworks site

Prerequisites

• Mathematical maturity; ability to follow proofs
• Linear algebra: vector and matrix algebra
• 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. At the end of the course there will be a few lectures of project presentations by students.

Readings will consist of a mixture of textbooks and course notes, which will be uploaded after lectures.

Students will complete a project, which should be done in groups of 3-6 students (project grading will be done proportional to group size). Special permission is needed to do a 1-2 person project, and it must be an ambitious research-oriented project.

Grading will be as follows:

• 35% final project write-up
• 20% homework (there will be 4-5 homeworks)
• 30% midterm (MIDTERM WILL BE IN CLASS Oct 25th)
• 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 lectures notes! Anyone who discovers a mistake in the lecture notes 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 may also consider awarding 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
  • Combinatorial auctions and reallocation of radio spectrum
• 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 3-6 students. Smaller teams 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 (this part may be dropped due to the size of the class)

Tentative Schedule

Related Courses

Below is a list of related courses.