Dr. Jim Haglund, jhaglund@math.upenn.edu
Course webpage: http://www.math.upenn.edu/~jhaglund/432/

Office hours during finals week: Monday April 30, 9:00-9:50am and 1:00-1:45pm in DRL 4E2B.
Office Phone: 215-573-9093

Grader: John Cui, scui@wharton.edu
Office hour: M 3-4pm, DRL 4C11.

Lecture: MWF 12-12:50pm in DRL A5

Course: Game Theory. Game Theory is a relatively new and interesting mathematical discipline which has many applications to economics and other areas. This course covers standard topics in game theory such as combinatorial games, two person (zero-sum and general-sum) games, noncooperative games, and Nash's equilibrium theorem. We will focus on the mathematics involved.

Text: The text for this course is " Game Theory" by Thomas S. Ferguson, available free online at his UCLA webpage. Some auxillary sources which may be helpful to consult, on reserve in the Math/Physics Library in DRL 3N1, are "Winning Ways for your Mathematical Plays" by Berlekamp, Conway, and Guy, and "A Course in Game Theory" by M. J. Osborne and A. Rubenstein.

Exams and Grades: There will be two hour exams and a final exam. Each hour exam counts 25% of your grade, and the final exam counts 40%. HW counts 10%. Hour exam 1 will be on Wednesday, February 15, and Hour exam 2 will be on Wednesday, March 28. Both Hour exams are from 12-12:55pm in DRL A5.
The final exam is on Tuesday, May 1 from 9am-11am in DRL A8.
You have the option of doing a special report, roughly four pages in length, on the mathematics behind any topic in game theory. If you turn in a special report, I will take the maximum of your grade on the report and on the last section of the final exam (which is based on the last part of the book, and accounts for 15% of your class grade). The report is due Wednesday, May 2 by 6pm (slide it under the door of my office, DRL 4e2b).

Midterm 1: Covers all of Part I. Games you may be asked to find winning moves in include Nim, Fibonacci Nim, Lasker's Nim, Moore's Nim_k, Misere Nim, Dynamic Subtraction, Northcott's Game, Directed Graph Games, Kayles, Turtles, Twins, Mock Turtles, Ruler, Turning Corners, Tartan Games, Green Hackenbush, sums of games. You do not have to memorize SG-functions (they will be provided), but you may be asked to prove a given pattern holds using induction. You may also be asked to explain parts of any of the proofs of theorems discussed in class, such as the solution to Fibonacci Nim or the Tartan Theorem.

Midterm 2: Covers Sections 1 through 5 of Part II: Two-Person Zero-Sum Games. Topics include Strategic form of Games, Matrix Games: Saddle Points, Domination, Solving 2 by n and m by 2 games, Latin square games, Principle of Indifference, Nonsingular matrix games, Diagonal games and other special matrix games, Invariance, Best (or Bayes) response, Simplex (or pivot) method. Extensive form of a game.

Final Exam: Cummulative. Covers all of Part I, Sections 1 through 5 of Part II, and all of Part III. The Optional Secton on the final exam, where as described in class you can substitute your score on this section with your score on a report (roughly $4$ pages in length) on the mathematics of game theory, covers Part III.

Important Dates:
Monday January 16, Martin Luther King Day: No Classes.
Hour Exam 1: Wednesday, February 15, 12-12:55pm, DRL A5.
Last Day to Drop a Course: Friday, February 17
Spring Break: March 3-11
Hour Exam 2: Wednesday, March 28, 12-12:55pm in DRL A5.
Last Day of Class: Monday, April 22
Final Exam: Tuesday, May 1 from 9am-11am in DRL A8.

Homework Assignments:
No late HW accepted except for Dean's excuse.
HW (for Wednesday, Jan. 18, not to be turned in) Do problem 1.5#3, p. I-6.

HW1 due Monday 1/30 at beginning of lecture: 1.5#1, 1.5#7, pp. I-6, I-7 and 2.6#2, 2.6#5, 2.6#7 pp. I-11 to I-13.
HW1 Solutions

HW2 due Monday, Feb. 13 at beginning of lecture: 4.5#4, 4.5#5, pp. I-26, I-27, 5.5#1, 5.5#3, 5.5#8, pp. I-38, I-39 and 6.4#1, pp. I-45.
HW2 Solutions (plus a proof of the Tartan Theorem)

HW3 due Monday, March 12 at beginning of lecture: Part II: 1.5#2, 1.5#3, 2.6#2, 2.6#4, 2.6#7, 2.6#8, 3.7#1, 3.7#7, 3.7#15.
HW3 Solutions

HW4 due Monday, March 26 at beginning of lecture: Part II: 4.7#1, 4.7#2, 4.7#4, 5.9#1, 5.9#5, 5.9#7.
HW4 Solutions

HW5 due Monday, April 23 at beginning of lecture: Part III: 1.6#2, 2.5#1, 2.5#4, 2.5#7, 2.5#8, 3.5#2, 3.5#4, 3.5#5, 4.5#1, 4.5#5.
HW5 Solutions