**Course: MATH 167, Game Theory, Lecture 1, Winter 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:* 21 February 2016

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

**Office Hours:** Fridays, 9AM-11AM, MS 5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
11AM-1150AM, Geology 4645

**TA:** William Rosenbaum, wrosenbaum@math.ucla.edu

**TA Office Hours:** Mondays 1PM-2PM, MS 6603

**TA Course Website:** Here

**Discussion Session Meeting Time/Location:** Tuesday, 11AM-1150AM,
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,
January 25, 11AM-1150AM, Pub Aff 2214

**Second Midterm:** Friday, February 19, 11AM-1150AM, Pub Aff 1246

**Final Exam:** Friday, March 18, 8AM-11AM, Boelter 2444

**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 | Jan 4: 1.1, Impartial Games | Jan 5: Homework 0 (ungraded) | Jan 6: 1.1.1, 1.1.2, Chomp, Nim | Jan 8: 1.1.3, Sprague-Grundy Theorem | |

2 | Jan 11: 1.2, Partisan Games | Jan 12: Homework 1 due | Jan 13: 1.2.1, Hex | Jan 15: 2.1, Two-Person Zero Sum Games | |

3 | Jan 18: No class | Jan 19: Homework 2 due | Jan 20: 2.2, Minimax Theorem, Background | Jan 22: 2.2, Minimax Theorem | |

4 | Jan 25: Midterm #1 | Jan 26: No homework due | Jan 27: 2.3, Domination | Jan 29: Leeway | |

5 | Feb 1: 3.1, General Sum Games | Feb 2: Homework 3 due | Feb 3: 3.2, Nash equilibria | Feb 5: 3.3, Correlated equilibria | |

6 | Feb 8: 3.6, Fixed Point Theorems | Feb 9: Homework 4 due | Feb 10: 3.5, Nash's Theorem | Feb 12: 3.7, Evolutionary Game Theory | |

7 | Feb 15: No class | Feb 16: Homework 5 due | Feb 17: 3.8, Signaling and Asymmetric Information | Feb 19: Midterm #2 | |

8 | Feb 22: 4.1, Coalitions and Shapley Value | Feb 23: Homework 6 due | Feb 24: 5.1, Mechanism design | Feb 26: 5.2, Auctions | |

9 | Feb 29: 6.1,6.2, Social Choice | Mar 1: Homework 7 due | Mar 2: 6.3, Arrow's impossibility theorem | Mar 4: Influences, Fourier analysis | |

10 | Mar 7: Noise Sensitivity | Mar 8: Homework 8 due | Mar 9: Quantum Games | Mar 11: CHSH inequality, Bell's inequality |

**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.