Courses | Christian Kroer

Algorithmic Game Theory for OR

Wed, 03 Sep 2025 13:00:00 +0000

Course Info

Instructor: Christian Kroer
Time: Mondays & Wednesdays 10:10-11:25pm
Location: 337 Mudd
Office hours: Wednesday after class

Course Summary

This is a graduate-level course on Algorithmic Game Theory and Mechanism Design. We will cover some of the theoretical foundations of game theory and mechanism design, and cover a number of the most important AGT and MD algorithms that are used in practice. We will take a very optimization-centric view towards AGT, and indeed we will see that an optimization lens is a very fruitful perspective on AGT, both in theory and practice.

We will have about 24 lectures total.

We will describe several practical applications, including how to:

Fairly allocate course seats to students, food to food banks, etc
Protect wildlife or airports
Conduct auctions for Internet ads or electricity

Course Structure

The course will be lecture-based, with Christian Kroer giving the lectures. We will also have about seven guest lectures by Jakub Cerny. At the end of the course there will be a few lectures of project presentations by students.

Readings will consist of excerpts from several textbooks.

Students will complete a project, which may be done individually or in groups of 2-3 students.

Grading will be as follows:

65% final project write-up
20% Final project presentation
10% Participation
5% Project proposal

Prerequisites

This is intended to be a PhD-level course for students in Operations Research and adjacent areas such as computer science, economics, and statistics. The most important prerequisite is mathematical maturity. Students should have a strong foundation in optimization (including convex optimization and duality) and applied probability. Familiarity with basic concepts from algorithm design and analysis will be helpful. Students are expected to be comfortable with linear algebra, calculus, and some basic real analysis.

Students from outside OR may have less optimization background than will be assumed for the course. It should be possible for a mathematically-mature PhD student to pick up the necessary background as we go along.

Advanced undergrads and MS students may take the class pending discussion with me about having sufficient background (I will require you to have taken some PhD-level mathematics or optimization) and motivation for taking the course.

Textbooks

There is no single textbook that will cover everything in the course. We will use my textbook for a number of topics. Below I also list a few other books that we are likely to draw from.

Games, Markets, and Online Learning (CK). Christian Kroer (forthcoming in print March 2026).
Algorithmic Game Theory (AGT) by Nisan, Roughgarden, Tardos, and Vazirani.
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”).
A Modern Introduction to Online Learning (MIOL) by Orabona. Free.

Schedule

Date	Topic	Reading
9/3	Course intro + intro to GT	CK Ch 1
9/8	Canceled class due to getting sick
9/10	Intro to game theory	CK Ch. 2, AGT Ch 1, 2 (optional)
9/15	No-regret learning setup	CK Ch. 4, Orabona Ch. 6.0-6.4
9/17	No-regret learning: OMD and minimax thm	CK Ch. 4, Orabona Ch. 6.0-6.4
9/22	Self play	CK Ch. 6, 7 (optional)
9/24	Fixed-point theorems and existence	CK Ch. 10
9/29	Correlated equilibria	??
10/1	CCE and refinements	??
10/6	Auctions I	CK. 3, Krishna Ch. 3
10/8	Auctions II	CK. 3, Krishna Ch. 3
10/13	Single-parameter mechanism design	Krishna Ch. 5
10/15	Canceled class due to getting sick
10/20	General mechanism design	Krishna Ch. 5
10/22	Fisher markets	??
10/27	INFORMS	??
10/29	INFORMS	??
11/3	Voting day
11/5	Fair division	CK Ch. 11
11/10	Tatonnement, prop. response, Shmyrev	CK Ch. 12
11/12	Social choice	??
11/17	Social choice	??
11/19	Indivisible fair allocation	CK. Ch. 13
11/24	Energy markets	CK. Ch. 14
12/1	Finish energy markets, presentations	CK. Ch. 14
12/3	Project presentations
12/8	Project presentations

Below is a list of related courses at other schools.

Instructor	Title	Year	School
Gabriele Farina	Topics in Multiagent Learning	2023	MIT
John P. Dickerson	Mechanism Design	2022	UMD
Gabriele Farina & Tuomas Sandholm	Computational Game Solving	2021	CMU
Christian Kroer	Economics, AI, and Optimization	2020	Columbia
John P. Dickerson	Applied Mechanism Design for Social Good	2018	UMD
Fei Fang	Artificial Intelligence Methods for Social Good	2018	CMU
Yiling Chen	Topics at the Interface between Computer Science and Economics	2016	Harvard
Vincent Conitzer	Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design	2016	Duke
Sanmay Das	Multi-Agent Systems	2016	Wash U
Ariel Procaccia	Truth, Justice, and Algorithms	2016	CMU
Milind Tambe	Security and Game Theory	2016	USC
Constantinos Daskalakis	Games, Decision, and Computation	2015	MIT
Tuomas Sandholm	Foundations of Electronic Marketplaces	2015	CMU
Tim Roughgarden	Algorithmic Game Theory	2013	Stanford

AI, Games, and Markets - Fall 2024

Fri, 06 Sep 2024 13:00:00 +0000

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.
For IEOR undergraduate majors, it is strongly recommended that you take IEOR 3608 before this class, and ideally IEOR 3609 as well.

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)
13% midterm 1, 13% midterm 2, 14% final
5% Project proposal
5% Project milestone report
5% Final project presentation (I may drop presentations depending on how many groups there are)

Final grades are calculated as follows: a total score is calculated according to the percentages above. Based on these scores, grade cutoffs are chosen to very roughly match a 40%/40%/20% distribution on A/B/C (lower scores like D/F are only used if someone performs far below the rest of the class). For a small elective class such as this one, I may have more A and B scores than the typical 40/40/20 distribution suggests, since average student performance tends to be higher.

Exam dates: midterm 1 is Oct 9th, midterm 2 is Nov 6th, final is Dec 2nd or 4th.

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)
An Introduction to Game Theory by Martin J. Osborne.
Solutions for the Osborne book.

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 11th
A 2-page progress report is due November 25th
A 5-10 page whitepaper, formatted as a NeurIPS conference paper, is due December 22nd
Each team must make a ~10m presentation of their project

Tentative Schedule

Date	Topic	Reading
9/4	Course intro	CK Ch 1
9/9	Intro to game theory	CK Ch. 2, AGT Ch 1, 2 (optional)
9/11	Continue GT intro
9/16	Intro to auctions	CK Ch. 3, AGT Ch 9, 10
9/18	Continue auctions
9/23	Regret minimization	CK Ch. 4 (you may skip the proofs of Theorems 7 and 8)
9/25	Continue regret
9/30	Nash eq. from regret min.	CK Ch. 6
10/2	Extensive-form games intro	CK Ch. 8 (8.5-8.6 optional), AGT 3.1-3.2, 3.7 - 3.11 (optional)
10/7	Continue EFG intro
10/9	Midterm I
10/14	Fair division	CK. Ch 10
10/16	Continue fair division
10/21	Fair indivisible allocation	CK. Ch 11
10/23	Position auctions	CK. Ch 12
10/28	Auctions with Budgets	CK. Ch 13, Sec 13.1-13.4
10/30	continue budgets
11/4	Election holiday
11/6	Midterm II
11/11	Demographic Fairness	CK. Ch 15
11/13	Stackelberg Equilibrium	CK. Ch 16
11/18	SE + Security Games	CK. Ch 16
11/20	Fair Combinatorial Allocation	CK. Ch 17
11/25	Electricity Markets Intro	CK. Ch. 19
11/27	Thanksgiving holiday
12/2	Electricity Markets - Unit Commitment	CK. Ch. 20
12/4	Final exam
12/9	Project Presentations

Below is a list of related courses.

Instructor	Title	Year	School
Gabriele Farina	Topics in Multiagent Learning	2023	MIT
John P. Dickerson	Mechanism Design	2022	UMD
Gabriele Farina & Tuomas Sandholm	Computational Game Solving	2021	CMU
Christian Kroer	Economics, AI, and Optimization	2020	Columbia
John P. Dickerson	Applied Mechanism Design for Social Good	2018	UMD
Fei Fang	Artificial Intelligence Methods for Social Good	2018	CMU
Yiling Chen	Topics at the Interface between Computer Science and Economics	2016	Harvard
Vincent Conitzer	Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design	2016	Duke
Sanmay Das	Multi-Agent Systems	2016	Wash U
Ariel Procaccia	Truth, Justice, and Algorithms	2016	CMU
Milind Tambe	Security and Game Theory	2016	USC
Constantinos Daskalakis	Games, Decision, and Computation	2015	MIT
Tuomas Sandholm	Foundations of Electronic Marketplaces	2015	CMU
Tim Roughgarden	Algorithmic Game Theory	2013	Stanford

AI, Games, and Markets - Fall 2023

Wed, 06 Sep 2023 13:00:00 +0000

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

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

Date	Topic	Reading
9/6	Course intro	CK Ch 1
9/11	Intro to game theory	CK Ch. 2, AGT Ch 1, 2 (optional)
9/13	Intro to auctions	CK Ch. 3, AGT Ch 9, 10
9/18	Regret minimization	CK Ch. 4 (you may skip the proofs of Theorems 7 and 8)
9/20	Nash eq. from regret min.	CK Ch. 5
9/25	Extensive-form games intro	CK Ch. 6 (6.5-6.6 optional), AGT 3.1-3.2, 3.7 - 3.11 (optional)
9/27	Continue EFG intro
10/2	Fair division	CK. Ch 7
10/4	Continue fair division
10/9	Fair indivisible allocation	CK. Ch 8
10/11	Position auctions	CK. Ch 9
10/16	Auctions with Budgets	CK. Ch 10, Sec 10.1-10.4
10/18	Demographic Fairness	CK. Ch 12
10/23	Stackelberg Equilibrium	CK. Ch 13
10/30	Security Games	CK. Ch 13
11/8	Fair Combinatorial Allocation	CK. Ch 14
11/15	Group 1on1 meetings
11/17	Group 1on1 meetings
11/20	Group 1on1 meetings
11/27	Electricity Markets Intro	CK. Ch. 16
11/29	Electricity Markets - Unit Commitment	CK. Ch. 17
12/4	Project Presentations
12/6	Project Presentations
12/11	Project Presentations

Below is a list of related courses.

Professor	Title	Year	School
Gabriele Farina	Topics in Multiagent Learning	2023	MIT
John P. Dickerson	Mechanism Design	2022	UMD
Gabriele Farina & Tuomas Sandholm	Computational Game Solving	2021	CMU
Christian Kroer	Economics, AI, and Optimization	2020	Columbia
John P. Dickerson	Applied Mechanism Design for Social Good	2018	UMD
Fei Fang	Artificial Intelligence Methods for Social Good	2018	CMU
Yiling Chen	Topics at the Interface between Computer Science and Economics	2016	Harvard
Vincent Conitzer	Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design	2016	Duke
Sanmay Das	Multi-Agent Systems	2016	Wash U
Ariel Procaccia	Truth, Justice, and Algorithms	2016	CMU
Milind Tambe	Security and Game Theory	2016	USC
Constantinos Daskalakis	Games, Decision, and Computation	2015	MIT
Tuomas Sandholm	Foundations of Electronic Marketplaces	2015	CMU
Tim Roughgarden	Algorithmic Game Theory	2013	Stanford

AI, Games, and Markets - Spring 2022

Tue, 18 Jan 2022 13:00:00 +0000

Course Summary

This is a course on how techniques from AI and optimization enable large-scale game solving and market design. 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 large-scale marketplaces such as internet advertising, recommender systems, and electricity markets. This is intended to be an advanced MS level and senior undergraduate course for students in Operations Research and Financial Engineering.

We will most likely cover the following applications:

How to make a go or poker AI
Market design for large-scale internet advertising auctions
Electricity market design

Admin stuff

Course Info

Instructor: Christian Kroer
Time: Mondays & Wednesdays 1:10-2:25pm
Location: 702 Hamilton Hall
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: derivates, optimality conditions, Lagrange multipliers
Optimization: linear programming, mixed-integer programming (this can potentially be learned along the way)

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

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:

Intro to game theory and market design
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
Electricity markets
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

Textbooks

The primary book is:

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.

Students are welcome to propose a topic of their own. Some project ideas can also be found on courseworks.

Project rules:

Teams should have 3-4 students. Smaller teams require instructor permission.
You must choose a project by March 23rd
A one-page project proposal is due March 25th
A 2-page midterm progress report is due April 15th
A 5-10 page whitepaper, formatted as a NeurIPS conference paper, is due May 8th
Each team must make a ~20m presentation of their project

Extremely Tentative Schedule

#	Date	Topic	Reading	Lecture notes
1	1 / 19	Course Intro		Lec. note 1
2	1 / 24	Intro to game theory and auctions	AGT Ch 1, 2	Lec. note 2
3	1 / 26	Intro to game theory and auctions	AGT Ch 9, 10	Lec. note 3
4	1 / 31	Regret Minimization	Lecture note (you may skip the proofs of Theorems 2 and 3)	Lec. note 4
5	2 / 2	Nash eq. from regret min.	Lect. Note 5	Lec. note 5
6	2 / 7	Extensive-Form Games Intro	AGT 3.1-3.2, 3.7 - 3.11	Lec. note 6
8	2 / 9	Continue EFG Intro, CFR	Lect. note 6, or this tutorial	same as above
8	2 / 14	CFR	Lect. note 6, or this tutorial	same as above
9	2 / 16	Fair Division	AGT Ch 5 & 6	Lec. note 7
10	2 / 21	Fair Indivisible Allocation		Lec. note 8
11	2 / 23	Continue fair allocation
12	2 / 28	Internet advertising auctions 1: position auctions	Ch. 15 of Easley and Kleinberg	Lec. note 9
13	3 / 2	Continue position auctions
14	3 / 7	Internet advertising auctions 2: budgets	Lec. note 10 Sec 1,2, and 3	Lec. note 10
15	3 / 9	Internet advertising auctions 3: online budget management	Lec. note 11	Lec. note 11
16	3 / 14	Spring break: no class
17	3 / 16	Spring break: no class
18	3 / 21	class canceled
19	3 / 23	Fairness in Ad Auctions	Lec. note 12	Lec. note 12
20	3 / 28	Electric Grid Operations	Lec. note 13	Lec. note 13
21	3 / 30	Electric Grid Pricing	Lec. note 13
22	4 / 4	Electric Grid Unit Commitment	Lec. note 14	Lec. note 14
23	4 / 6	Fair Combinatorial Allocation	Lec. note 15	Lec. note 15
24	4 / 11	Project 1on1 meetings
25	4 / 13	Project 1on1 meetings
26	4 / 18	Stackelberg Equilibrium	Lec. note 16	Lec. note 16
27	4 / 20	Stackelberg Equilibrium	Lec. note 16	Lec. note 16
28	4 / 25	Project presentations
29	4 / 27	Project presentations
30	5 / 2	Project presentations

Below is a list of related courses at other schools.

Professor	Title	Year	School
John P. Dickerson	Mechanism Design	2022	UMD
Gabriele Farina & Tuomas Sandholm	Computational Game Solving	2021	CMU
Christian Kroer	Economics, AI, and Optimization	2020	Columbia
John P. Dickerson	Applied Mechanism Design for Social Good	2018	UMD
Fei Fang	Artificial Intelligence Methods for Social Good	2018	CMU
Yiling Chen	Topics at the Interface between Computer Science and Economics	2016	Harvard
Vincent Conitzer	Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design	2016	Duke
Sanmay Das	Multi-Agent Systems	2016	Wash U
Ariel Procaccia	Truth, Justice, and Algorithms	2016	CMU
Milind Tambe	Security and Game Theory	2016	USC
Constantinos Daskalakis	Games, Decision, and Computation	2015	MIT
Tuomas Sandholm	Foundations of Electronic Marketplaces	2015	CMU
Tim Roughgarden	Algorithmic Game Theory	2013	Stanford

Economics, AI, and Optimization

Tue, 21 Jan 2020 13:00:00 +0000

Course Info

Instructor: Christian Kroer
Time: Mondays & Wednesdays 1:10-2:25pm
Location: 233 Mudd
Office hours: Wednesday 2:25-3:30pm (or anytime; but email me first in that case)

Course Summary

Economics, AI, and Optimization is an interdisciplinary course that will cover selected topics at the intersection of economics, operations research, and computer science. A recurring theme in the course will be how economic solution concepts are enabled at scale via AI and optimization methods. We will describe several successful practical applications, including how to:

Make a poker AI
Fairly allocate course seats to students, food to food banks, etc
Protect wildlife or airports
Conduct large-scale auctions for spectrum or Internet ads

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 may be done individually or in groups of 2-3 students.

Grading will be as follows:

50% final project write-up
20% homework (there will only be 1-2 homeworks)
15% Final project presentation
10% Participation
5% Project proposal

Outline

A rough outline is as follows:

Intro to game theory and market design
Nash equilibrium
- Zero-sum games, minimax theorem
- First-order methods/Online convex optimization/regret minimization in games
- Deep learning for solving games at scale
- How the above is used in making superhuman poker AIs
Security games
- Stackelberg equilibrium
- Basic Stackelberg security game model
- Mixed-integer programming, deep learning for scaling up
- Applications to airport, wildlife, power grid security
Market design
- Fisher markets and market equilibrium
- Optimization methods for computing market equilibria
- Machine learning methods for large markets
- fair division, course allocation
- Internet ad auctions
- Spectrum auctions

We will also cover some subset of the following:

Matching markets
Data science in multiagent systems

Textbooks

The primary book is:

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)

Schedule

#	Date	Topic	Reading	Lecture notes
1	1 / 22	Introduction	AGT Ch 1	Lecture note 1.pdf
2	1 / 27	Introduction to game theory	AGT Ch 1, Hazan Ch 1	Lecture note 2.pdf
3	1 / 29	Hedge, Online convex optimization	Hazan Ch 1, Ch 5.0-5.4	Lecture note 3.pdf
4	2 / 3	Online Mirror Descent	Orabona Ch. 6.0-6.4	See previous note
5	2 / 5	OMD convergence, Minimax theorem	Orabona Ch. 6.0-6.4	See previous note
6	2 / 10	Blackwell approachability, regret matching	Farina blog	Lecture note 4.pdf
7	2 / 12	From Regret to Nash		Lecture note 5.pdf
8	2 / 17	Extensive-Form Games, DGFs	AGT Ch 3.7 - 3.11	Lecture note 6.pdf
9	2 / 19	Counterfactual Regret Minimization		See previous note
10	2 / 24	Subgame solving, deep learning	BS18 Sections 1 and 2 (preferably whole paper), BSA18 Section 2 (preferably whole paper), DeepStack sections “DeepStack” and “Deep Counterfactual Value Networks”	Lecture note 7.pdf
11	2 / 26	Stackelberg Equilibrium, Security Games		Lecture note 8.pdf
12	3 / 2	Stackelberg wrap-up, Intro to Fair Division	HCSC Ch 11	Lecture note 9.pdf
13	3 / 4	Eisenberg-Gale convex program	AGT Ch 5 & 6	See previous note
14	3 / 11	Dominant-Resource Fairness		Lecture note 10.pdf
15	3 / 30	Intro to Auctions	AGT Ch 9 & 10	Lecture note 11.pdf
16	4 / 1	Auctions with Budgets - Second Price	Multiplicative Pacing Equilibria in Auction Markets	Lecture note 12.pdf
17	4 / 6	Auctions with Budgets - First Price	Pacing Equilibrium in First-Price Auction Markets	Lecture note 12.pdf
18	4 / 8	Auctions with Budgets - Dynamics	Learning in Repeated Auctions	Lecture note 13.pdf
19	4 / 13	Large-Scale Market equilibrium		Lecture note 14
20	4 / 15	Large-Scale Market equilibrium		See previous note
21	4 / 20	Large-Scale Market equilibrium		See previous note
22	4 / 22	Indivisible Goods - Fair Division	For trying fair division: http://www.spliddit.org/	Lecture note 15
23	4 / 27	Indivisible Goods - Fair Division Algorithms		See previous note
24	4 / 29	Indivisible Goods - A-CEEI		See previous note
25	5 / 4	Indivisible Goods - A-CEEI		See previous note

Below is a list of related courses at other schools.

Professor	Title	Year	School
John P. Dickerson	Applied Mechanism Design for Social Good	2018	UMD
Fei Fang	Artificial Intelligence Methods for Social Good	2018	CMU
Yiling Chen	Topics at the Interface between Computer Science and Economics	2016	Harvard
Vincent Conitzer	Computational Microeconomics: Game Theory, Social Choice, and Mechanism Design	2016	Duke
Sanmay Das	Multi-Agent Systems	2016	Wash U
Ariel Procaccia	Truth, Justice, and Algorithms	2016	CMU
Milind Tambe	Security and Game Theory	2016	USC
Constantinos Daskalakis	Games, Decision, and Computation	2015	MIT
Tuomas Sandholm	Foundations of Electronic Marketplaces	2015	CMU
Tim Roughgarden	Algorithmic Game Theory	2013	Stanford

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