# Economics, AI, and Optimization

### 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 / 1 | Auctions with Budgets - First Price | Pacing Equilibrium in First-Price Auction Markets | Lecture note 12.pdf |

### Related Courses

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 |