Topics in Statistics for Undergraduates:
Game Theory
STAT 490, Spring 2008

Mondays and Wednesdays
12:30 -- 1:20 PM in MATH 731

Professor: Mark Daniel Ward
Office: MATH 540
Phone: 765-496-9563

Text: Game Theory by Thomas S. Ferguson, available at no cost, online at UCLA. Based on past experience, we should be able to cover almost all of the material in Ferguson's book during one semester.

Course description: We analyze a wide variety of games by studying several mathematical models, including combinatorial games, two person (zero-sum and general-sum) games, noncooperative games, and Nash equilibrium. The interdisciplinary approach will be appealing to students in business, computer science, economics, mathematics, political science, statistics, etc.

STAT 490 is a "Topics in Statistics Course for Undergraduates". This particular version of STAT 490 is a guided reading course. Outside of class, students will study the game theory material independently or in groups. Students will meet as a group with Dr. Ward twice per week. Students are also welcome to see Dr. Ward outside of class during arranged or walk-in appointments. Dr. Ward will not give daily lectures but rather will guide the students through an introduction to combinatorial game theory (approximately 1/4 of the course content) and von Neumann style game theory (approximately 3/4 of the course content). The course is intended as an opportunity for students to have a somewhat independent learning experience, assisted by a professor, in an introduction to the very exciting world of game theory!

Attendance: Attendance counts as 29 percent of the overall grade. Each of the 29 days is worth 1 percent. Excused absences are approved in only rare cases, such as: the death of a family member; religious (or similar) observances; or mandatory attendance at an official Purdue event. Please contact the Dr. Ward at least one week in advance of any planned events.

Homework: Homework counts as 50 percent of the overall grade. Homework assignments will be given on a daily basis but will not be collected by Dr. Ward. Instead, students will be selected randomly (using, for instance, a 10-sided die). The chosen student will present her or his solution to a problem, along with justification or explanation for the solution if requested by the other students or by Dr. Ward. Since students are selected randomly to give their answers, the average homework score will be used as this portion of the grade.

Project: A project counts as 21 percent of the overall grade. Each student should consult with Dr. Ward sometime during the course about a suitable, independent project to complete. The content may be selected from either combinatorial or von Neumann style games. The project should consist of approximately ten pages (single-spaced lines, 12 point font) on a topic that is either (i) not covered, or (ii) only introduced but not explored in-depth, during the course.

Academic adjustments: Please refer all cases to the Office of the Dean of Students in Schleman Hall.

Nondiscrimination: Purdue University prohibits discrimination against any member of the University community on the basis of race, religion, color, sex, age, national origin or ancestry, marital status, parental status, sexual orientation, disability, or status as a veteran. Dr. Ward intends for STAT 490 to be welcoming and fair for all students.

Outline of Topics
Week 1: Mon, Jan 7
Section I.1
HW #1: Problems 1, 2, 4
challenge problem: 6
Wed, Jan 9
Section I.2
HW #2: Problems 2, 3, 5, 7a
challenge problem: 4ab
Week 2: Mon, Jan 14
Section I.3
HW #3: Problems 1, 2, 3, 5
Wed, Jan 16
Section I.4
Practiced sums of combinatorial
games in class, on chalkboard
Week 3: Mon, Jan 21
Rev. Dr. Martin Luther King, Jr., Day
Wed, Jan 23
Class cancelled.
Watch "A Beautiful Mind" at 8 PM.
Week 4: Mon, Jan 28
Section II.1
HW #4: Problems 2, 3, 4
Wed, Jan 30
Section II.2
HW #5: Problems 2, 4, 5, 6
Week 5: Mon, Feb 4
Section II.3
HW #6: Problems 1, 2, 3, 8
Maple example
Wed, Feb 6
Section II.4
HW #7: Problem 4
Week 6: Mon, Feb 11
Section II.5
HW #8: Problems 2, 3, 7ab
Wed, Feb 13
Section II.5 (continued)
HW #9: Problem 5
Week 7: Mon, Feb 18
Section III.1
HW #10: Problems 1, 2
Wed, Feb 20
Section III.2
HW #11: Problems 4, 5, 6, 8
Week 8: Mon, Feb 25 Wed, Feb 27
Week 9: Mon, Mar 3 Wed, Mar 5
Spring Break: Mon, Mar 10 Wed, Mar 12
Week 10: Mon, Mar 17
Section III.3
HW #12: Problems 1, 4
Wed, Mar 19
Section III.4
HW #13: Problems 1, 2, 3
Week 11: Mon, Mar 24
Section III.4
HW #14: Problem 4
Wed, Mar 26
Section IV.1
HW #15: Problem 1
Week 12: Mon, Mar 31
Section IV.2
HW #16: Problem 3
Wed, Apr 2
Class cancelled.
Dinner at Ward home on Friday, Apr 4
Watch "21" after dinner.
Week 13: Mon, Apr 7
Section IV.3
HW #17: Problems 2, 6
Wed, Apr 9
Week 14: Mon, Apr 14 Wed, Apr 16
Week 15: Mon, Apr 21 Wed, Apr 23