**Course: MATH 167, Game Theory, Lecture 1, Spring 2016**

**Prerequisite:** Math 115A.

**Course Content:** 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, social choice theory, and quantum games.

*Last update:* 24 May 2016

**Instructor:** Steven Heilman, heilman(@-symbol)ucla.edu

**Office Hours:** Wednesdays 11AM-12PM, 1PM-2PM, Fridays 11AM-12PM,
MS 5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
10AM-1050AM, Geology 4645

**TA:** Brent Woodhouse, bwoodhouse729(@-symbol)math.ucla.edu

**TA Office Hours:** Mondays 1PM-2PM, Thursdays 10AM-11AM, MS 6153

**TA Course Website:**

**Discussion Session Meeting Time/Location:** Tuesday, 10AM-1050AM,
Geology 4645

**Required Textbook:** Yuval Peres,
Game Theory, Alive. (The book is freely available
online)

**Other Textbooks (not required):** __Game Theory__, Maschler, Solan and Zamir. Compared to the book of 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 such as 131A, 131B and 131C.

See also the Game Theory book of Thomas S. Ferguson

A more recent draft of the textbook Game
Theory, Alive, by Anna R. Karlin and Yuval Peres, is
also available online, with a more comprehensive treatment and less typos,
though probabilistic notation is used. Since probability is not a
prerequisite for this class, we will not use this more recent draft
version. If you have taken probability, you may prefer this version
of the book, though.

**First Midterm:** Monday,
April 18, 10AM-1050AM, PAB 1434A

**Second Midterm:** Friday, May 13, 10AM-1050AM, PAB 1434A

**Final Exam:** Wednesday, June 8, 1130AM-230PM, PAB 1434A

**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 heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.

- Late homework is not accepted.
- If you still want to turn in late homework, then the number of minutes late, divided by 10, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 8 homework assignments, assigned weekly on Tuesday and
turned
in at the
**beginning**of the discussion section on the following Tuesday. - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Homework solutions will be posted on Friday after the homework is turned in.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, 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.
- We will use the MyUCLA gradebook.
- 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.
- You must attend the final exam to pass the course.

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

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Mar 28: 1.1, Impartial Games | Mar 29: Homework 0 (ungraded) | Mar 30: 1.1.1, 1.1.2, Chomp, Nim | Apr 1: 1.1.3, Sprague-Grundy Theorem | |

2 | Apr 4: 1.2, Partisan Games | Apr 5: Homework 1 due | Apr 6: 1.2.1, Hex | Apr 8: 2.1, Two-Person Zero Sum Games | |

3 | Apr 11: 2.2, Minimax Theorem, Background | Apr 12: Homework 2 due | Apr 13: 2.2, Minimax Theorem | Apr 15: 2.3, Domination | |

4 | Apr 18: Midterm #1 | Apr 19: No homework due | Apr 20: Leeway | Apr 22: 3.1, General Sum Games | |

5 | Apr 25: 3.2, Nash equilibria | Apr 26: Homework 3 due | Apr 27: 3.3, Correlated equilibria | Apr 29: 3.6, Fixed Point Theorems | |

6 | May 2: 3.5, Nash's Theorem | May 3: Homework 4 due | May 4: 3.7, Evolutionary Game Theory | May 6: 3.8, Signaling and Asymmetric Information | |

7 | May 9: 4.1, Coalitions and Shapley Value | May 10: Homework 5 due | May 11: 5.1, Mechanism design | May 13: Midterm #2 | |

8 | May 16: 5.2, Auctions | May 17: Homework 6 due | May 18: 6.1,6.2, Social Choice | May 20: 6.3, Arrow's impossibility theorem | |

9 | May 23: Influences, Fourier analysis | May 24: Homework 7 due | May 25: Noise Sensitivity | May 27: Quantum Games | |

10 | May 30: No class | May 31: Homework 8 due | Jun 1: CHSH inequality, Bell's inequality | Jun 3: Review of 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. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.