Course: Math 499, Game Theory, Spring 2025
Recommended Prerequisite: 1 from [Math 407 or Math 307] and 1 from [Math 225 or Math 235].
Course Content: This course will present the mathematics of game theory, i.e. the quantitative modeling of strategic interaction. Topics include: impartial games, partisan games, zero sum games, von Neumann's Minimax Theorem, general sum games, Nash equilibrium, fixed point theorems, evolutionary game theory, signaling, coalitions, auctions, and social choice theory. Time permitting, we will cover quantum games, algorithmic game theory, and applications of game theory to neural networks, such as generative adversarial networks or Monte Carlo Tree Search. The target audience of this course is advanced undergraduate students in mathematics, economics, computer science, or related fields, with an interest in a mathematically focused course on game theory.
Last update: 10 October 2024

Instructor: Steven Heilman, stevenmheilman(@-symbol)gmail.com
Office Hours: Fridays, 1030AM-12PM, Mondays, 1130AM-12PM, KAP 406G
Lecture Meeting Time/Location: Mondays, Wednesdays, and Fridays, 12PM-1250PM, GFS 105

Textbook: The following textbook is recommended but not required.
Karlin and Peres, Game Theory, Alive.
Some other non-required textbooks: Game Theory, Maschler, Solan and Zamir. Compared to the book of Karlin-Peres, this book is larger and more comprehensive. However, it is also a more advanced textbook, so it might be difficult to read if you have not taken several advanced math classes. See also the A course in game theory book of Thomas S. Ferguson

Exam 1: Wednesday, February 19, 12PM-1250PM, GFS 105
Exam 2: Friday, March 28, 12PM-1250PM, GFS 105
Final Exam: Friday, May 9, 11AM-1PM, GFS 105
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments

Email Policy:

• My email address for this course is stevenmheilman@gmail.com
• It is your responsibility to make sure you are receiving emails from stevenmheilman@gmail.com , and they are not being sent to your spam folder.
• Do NOT email me with questions that can be answered from this syllabus.

Extra Credit Project: There will be an optional extra credit project, where students will create a computer program that plays Nash's game of Hex in Python, and the top performers of a tournament will be awarded around 1% to 3% extra credit points for the course. The project would be due in the last week of class, and the ``finals'' of the tournament would occur in class during this time as well. Students can work in groups of up to three, and if a team wins some amount of extra credit, that credit will be split evenly among the participants. Since I will be running the finals on a Microsoft Surface Tablet (without much memory or processing power), you should not use too many extra Python packages beyond some standard ones. The code defining the game is HERE. The code is currently set up so that player 1 is playing a "blocking" type of strategy, while player 2 is just making random available moves. Your first task is to build a program that can beat player 1's blocking type strategy, in at least, say, 80 percent of games, while your program acts as the second player.

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
https://osas.usc.edu/
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)
OSASFrontDesk@usc.edu

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the Office of Equity and Diversity http://equity.usc.edu/ or to the Department of Public Safety http://capsnet.usc.edu/department/department-public-safety/online-forms/contact-us. This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. The Center for Women and Men http://www.usc.edu/student-affairs/cwm/ provides 24/7 confidential support, and the sexual assault resource center webpage sarc@usc.edu describes reporting options and other resources.

Exam Resources: Here are the exams and solutions I used when I last taught this class: Exam 1, Exam 1 Solution, Exam 2, Exam 2 Solution, Final, Final Solution, Exam 1, Exam 1 Solution, Exam 2, Exam 2 Solution, Final, Final Solution, Here is a page containing practice exams for another game theory class. Here is a page containing practice exams for another game theory class. Here is a page containing a practice midterm for another game theory class. Here is a page containing a practice final for another game theory class. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order.

Homework Policy:

• Homeworks are due at 11:59PM Thursdays.
• Homeworks are submitted in brightspace. To avoid internet issues, I recommend making your first submission of an assignment well in advance of the deadline.
• Homeworks should be submitted as single PDF documents. One way to create a PDF document from paper homework assignments is the freely available Adode Scan App
• Late homework is not accepted.
• If you still want to turn in your homework late, then the number of minutes late divided by ten will be deducted from the homework score.  The exact deduction and rounding procedure is not guaranteed to be accurate.
• The lowest homework score will be dropped. This policy is meant to account for illnesses, emergencies, dropped internet connections, etc.
• You may not use the internet to try to find answers to homework problems.
• Do not submit homework via email.
• Collaboration on homeworks is allowed and encouraged.
• All homework assignments must be written by you, i.e. you cannot copy someone else`s solution verbatim.

Grading Policy:

• The final course grade is weighted as the larger of the following two schemes.
  • Scheme 1: class participation (3%), homework (17%), the first midterm (20%), the second midterm (25%), and the final (35%).
  • Scheme 2: class participation (3%), homework (17%), the largest midterm grade (30%), and the final (50%).
  The grade for the semester will be curved. However, I do not "curve down" since anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
• If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
• Class participation is not the same as attendance.  I will never explicitly take attendance, but I will notice if someone is frequently absent.  Things that increase your class participation grade include: asking good questions, paying attention in class, showing up on time or early to class, etc. Things that decrease your class participation grade include: excessive talking or disruptions during class, frequent absences, excessive texting/smartphone usage in class, frequent tardiness, etc.
• You must take the final exam to pass the course.

Tentative Schedule: (This schedule may change slightly during the course.)

Advice on succeeding in a math class:

• Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
• When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
• Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
• Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
• If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

Homework

• HW1 HW2 HW3 HW4 HW5 HW6 HW7 soln

Homework .tex files

• HW1 HW2 HW3 HW4 HW5 HW6 HW7

Exam Solutions

• Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution

Supplementary Notes

• 499 Lecture Notes