CS 639 section 006: Topics in Game Theory and Learning (Fall 2025)

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 ENGR HALL 2255
Instructor: Professor Jerry Zhu, jerryzhu@cs.wisc.edu
Office hours: Thursdays 4-5pm in Morgridge Hall 5520

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 [KP]
   Algorithmic Game Theory, ed. Nisan, Roughgarden, Tardos, Vazirani [NRTV] 
   Tim Roughgarden's lecture notes on Algorithmic Game Theory

Discussions: piazza

Topics
2025-9-4 Class logistics, general sum games, dominant strategy (KP 4, 2.4.3, NRTV 1)
2025-9-9 Nash equilibrium (KP 4, NRTV 1) 
2025-9-11 indifference lemma (KP 4, NRTV 1) 
2025-9-16 finding mixed NE (KP 4, NRTV 1) 
2025-9-18 Potential games (KP 4.4, NRTV 19)
2025-9-23 Best response dynamics (KP 4.4, NRTV 19)
2025-9-25 Price of anarchy/stability (KP 8, NRTV 17, 18)
2025-9-30 PoA in market sharing (KP 8, NRTV 17, 18)
2025-10-2 PoA in routing (KP 8.1, NRTV 17, 18)
2025-10-7 PoS in network forming (KP 8.2, NRTV 17, 18)
2025-10-9 safety strategy, Two-player zero-sum games, minimax theorem (KP 2, NRTV 1) 
2025-10-14 Linear program for zero-sum games (KP Appendix A)
Extensive form games, imperfect and incomplete information (KP 6)
Correlated and coarse correlated equilibrium (KP 7.2, NRTV 1, R 13.3) 
Cooperative games, the core, Sharpley value, Nash bargaining (KP 12, NRTV 15)
Evolutionary game theory (KP 7.1, 18.1) 
Online learning (KP 18.3, NRTV 4)
Minimax theorem proof (KP 18.4, NRTV 4)
No-regret dynamics converge to CCE (R 17.3, NRTV 4)
midterm exam
Swap regret converges to CE (KP 18, NRTV 4)
Mechanism design, second price auction (KP 14)
VCG mechanism (KP 16.1, 16.2, NRTV 9)
Myerson's lemma (KP 15, NRTV 9)
Stable matching (KP 10, NRTV 10)

Grading: Class participation: 20%, Midterm exam: 40%, Final exam: 40%.

Midterm exam: in-class on Tuesday Oct. 21, 2025.

Final exam: 10:05AM - 12:05PM on 12/12/2025, Friday, room TBD by the university

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.