CS 639: Topics in Game Theory and Learning (Fall 2024)

Overview: Game theory is a mathematical framework to study interactions between multiple strategic agents, 
where agents view these interactions as "games" they are trying to "win". Mechanism design studies the design 
of such interactions so as to obtain socially desirable outcomes. Machine learning deals with growing experience 
by playing games.  In this class, we introduce these topics and connect them through the lens of a computer scientist. 
This class is primarily targeted towards advanced undergraduate and early graduate students with a strong background 
in mathematics and algorithms.

Lectures: Tu, Th 9:30-10:45 in EDUC SCI 301
Instructor: Professor Jerry Zhu, jerryzhu@cs.wisc.edu
Office hours: Thursdays 4-5pm in Computer Science 5381

Prerequisites: CS240, CS475, Econ301, or Econ 311.  We will use tools from calculus, probability, statistics, 
optimization, algorithms, and machine learning.  It is the student's responsibility to have an adequate background 
in these areas.  Students are expected to be comfortable with mathematical proofs and logical reasoning.

Textbook: Game Theory, Alive by Anna Karlin and Yuval Peres, denoted KP below. 
Other recommended reading: 
   Tim Roughgarden's lecture notes on Algorithmic Game Theory
   Stanford's Game Theory Online

Discussions: piazza

Tentative schedule, subject to change
Unit 1: Game Theory
9/5     introduction (KP 2.1)
9/10,12 two-player zero sum games, Von Neumann's minimax theorem (KP 2.2-2.6)
9/17,19 Nash equilibrium, linear program (KP appendix A)
9/24,26 general-sum games (KP 4-4.3, 4.5), dominant strategy (KP 2.4.3)
10/1,3  potential games, best response dynamics (KP 4.4)
10/8,10 extensive form games, imperfect and incomplete information (KP 6)
10/15,17 correlated equilibrium (KP 7.2, R lecture 13 section 3)
Unit 2: Mechanism
10/22,24 in-class midterm, the price of anarchy and stability (KP 8)
10/29,31 cooperative games, the Sharpley value (KP 12-12.3)
11/5,7 auction (KP 14.1, 14.2)
11/12,14 VCG (KP 15.1-15.4, 16.1, 16.2)
Unit 3: Learning
11/19,21 evolutionary game theory (KP 7.1, 18.1)
11/26 no-regret learning (KP 18.3)
12/3,5 minimax theorem (KP 18.4)
12/10 review

Grading: Homeworks: 60%, Midterm exam: 20%, Final exam: 20%.

Homework There will be around 10 homeworks, assigned in canvas. To be done individually. Do not use AI.  
Do not post homework questions to any websites.  Each homework has a strict deadline (typically one week after 
being assigned). You will not be able to submit the homework after the deadline.  However, we drop two lowest 
homework scores for final grade computation; these are meant for emergencies, use them strategically. Consequently, 
no late days are given.

Midterm exam: in-class on Tuesday Oct. 22, 2024.

Final exam: 12/17/2024, Tuesday 12:25PM - 2:25PM in SOC SCI 6102

A make-up exam will be offered only for documented emergencies and travel to academic conferences. The decision 
to accommodate a make-up exam will be at the discretion of the instructor.

Please read the university's policy on academic misconduct.