ECON 473 / STAT 473 - Game Theory
University of Illinois - Chicago
Spring 2021

This course serves as a rigorous introduction to game theory. We will cover static and dynamic games, pure and mixed strategies, and and situations with perfect and imperfect information. We will cover the foundationa theorems, including the celebrated von Neumann's minimax and Nash's equilibrium theorems. We will also consider economic, political, and biological applications.

Basic Information

Syllabus: pdf
Time and Location: T, R 9:30-10:45am online
Instructor: Lev Reyzin, SEO 418, (312)-413-3745
Instructor Office Hours: T 8:00-8:50am, R 11:00-11:50am online
TA: Nurlan Abdukadyrov
TA Office Hours R 8:30-9:20am
Textbook: Anna Karlin and Yuval Peres Game Theory, Alive (also available free online)

Exam Dates

Midterm: Tuesday March 9th (scheduled for 9:30-10:45am)
Final Exam: Wednesday May 5th (scheduled for 10:30am-12:30pm)

Problem Sets

problem set 1 due 2/4/21
problem set 2 due 2/25/21
problem set 3 due 4/1/21
problem set 4 due 4/20/21
problem set 5 due 4/29/21

Lectures and Readings

Note: lectures will have material not covered in the readings.

Lecture 1 (1/12/21)
covered material: intro to the course, discussion of what are games
reading: preface

Lecture 2 (1/14/21)
covered material: introduction to zero-sum games, payoff guarantee inequality
reading: 2.1

Lecture 3 (1/19/21)
covered material: mixed strategies and expected payoffs, probability simplex, safety strategies
reading: 2.2

Lecture 4 (1/21/21)
covered material: minimax theorem, equalizing payoffs
reading: 2.3

Lecture 5 (1/26/21)
covered material: saddle points, domination
reading: 2.4

Lecture 6 (1/28/21)
covered material: submarine salvo, Nash equilibria in zero-sum games
reading: 2.5

Lecture 7 (2/2/21)
covered material: general-sum games, Prisoner's dilemma
reading: 4.1

Lecture 8 (2/4/21)
covered material: Nash equilibria in general two-player games, the game of chicken
reading: 4.2

Lecture 9 (2/9/21)
covered material: general-sum games with more than two players, Nash equilibria in many-player games
reading: 4.3 up to (but not including) 4.3.1

Lecture 10 (2/11/21)
covered material: symmetric general-sum games
reading: 4.3.1

Lecture 11 (2/16/21)
covered material: potential games, with conjection game example
reading: 4.4

Lecture 12 (2/18/21)
covered material: consensus game example, infinite games, tragedy of commons, market for lemons
covered material 4.5, 4.6

Lecture 13 (2/23/21)
covered material: proof of minimax theorem and relationship to LP, video by Roughgarden (asynchronous)
optional reading: 2.6

Lecture 14 (2/25/21)
covered material: introduction to evolutionary game theory
reading: 7.1 up to (but not including) 7.1.2

Lecture 15 (3/2/21)
covered material: evolutionarily stable strategies, population invasion
reading: 7.1.2

Lecture 16 (3/4/21)
covered material: midterm review
reading: review 2.1-2.5 (recall that 2.6-2.7 will not be on the exam), 4.1-4.6

Lecture 17 (3/9/21)
midterm exam: no lecture

Lecture 18 (3/11/21)
covered material: correlated equilibria, battle of the sexes, chicken revisited
reading: 7.2

Lecture 19 (3/16/21)
covered material: introduction to extensive form, zero sum extensive form games, backward induction, subgame-perfect NE
reading: begin 6.1

Lecture 20 (3/18/21)
covered material: non-zero sum games in extensive form, line-item veto, mutually assured destrtuction, centipede
reading: finish 6.1

Lecture 21 (3/30/21)
covered material: extensive-form games of imperfect information, chicken revisited
reading: 6.2

Lecture 22 (4/1/21)
covered material: introduction to games of incomplete information, Bayesian games in extensive form
reading: 6.3.1

Lecure 23 (4/6/21)
covered material: signaling, zero-sum games in extensive form
reading: 6.3.2 - 6.3.4

Lecture 24 (4/8/21)
covered material: repeated games with discounting, Tit-for-Tat
reading: 6.4.1

Lecture 25 (4/13/21)
covered material: intro to combinatorial games as sepcial case of extensive form games, subtraction game reading: 1.1 up to (but not including) 1.1.1

Lecture 26 (4/15/21)
covered material: chomp, partisan games, tic-tac-toe, hex, strategy stealing again
reading: 1.2

Lecture 27 (4/20/21)
covered material: computational aspects of combinatorial games, AlphaGo
optional reading: a blog post by Demis Hassabis

Lecture 28 (4/22/21)
covered material: the price of anarchy, selfish routing, and the Braess paradox
reading: 8.1