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 and Go. 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: TBD
• Office hours: Wednesday 2:25-3:30pm Mudd 314
• 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)

Everything after this point should be considered tentative

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 2-4 students. Special permission is needed to do an individual project.

Grading will be as follows:

• 50% final project write-up
• 25% homework (there will be 4-5 homeworks)
• 5% Project proposal
• 5% Project milestone report
• 5% Final project presentation
• 10% Participation

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). 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 your feedback

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 (the exact ordering may change):

• Intro to game theory and market design
• Nash equilibrium
  • Zero-sum games, minimax theorem
  • No-regret learning
  • Perfect-information games and go AIs, Monte Carlo tree search
  • Imperfect-information games and poker AIs
  • Deep learning for solving games at scale
• Security games with applications to airport, wildlife, power grid security
• Market design and the internet
  • Internet advertising auctions
  • Recommender systems
  • Bias and fairness in machine learning and internet advertising
• Fair Resource Allocation
  • Fair division via competitive equilibria
  • Fair course seat allocation
  • Allocating food to food banks

Textbooks

The primary will be my lecture notes. I will also assign complementary reading from:

• 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)

Project

Students will complete a semester-long 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 teams require instructor permission.
• You must choose a project by October 23rd
• A one-page project proposal is due October 29th
• A 2-page midterm progress report is due November 17th
• 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

Extremely Tentative Schedule

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