Topics in Statistics for Undergraduates:
Game Theory
STAT 490, Spring 2009

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 an independent reading course. Students will study the game theory material independently. Students will meet with Dr. Ward once per week. Students are also welcome to see Dr. Ward during other arranged or walk-in appointments. Dr. Ward will not give daily lectures but rather will mentor the students as they read 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 an independent learning experience, assisted by a professor, in an introduction to the very exciting world of game theory!

Attendance: Attendance counts as 32 percent of the overall grade. Each of the 16 weekly meetings is worth 2 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 32 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 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 18 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.

Final Exam: The final exam counts as 18 percent of the overall grade.

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 12
I.1, HW: 1, 2, 4, (and try 6 too)
I.2, HW: 2, 3, 4, 5, 7a
Wed, Jan 14 Fri, Jan 16
Week 2: Mon, Jan 19 (no meeting)
Rev. Dr. Martin Luther King, Jr., Day
Wed, Jan 21
I.3, HW: 1, 2, 3, 5
I.4, HW: 1, 2, 3, 4, 5, 10
Fri, Jan 23
Week 3: Mon, Jan 26
I.5, HW: 1abcd, 2abc
Wed, Jan 28 Fri, Jan 30
Week 4: Mon, Feb 2
II.1, HW: 1, 3
Wed, Feb 4 Fri, Feb 6
Week 5: Mon, Feb 9
II.2, HW: 1, 3, 4, 5, 6, 7, 8
Wed, Feb 11 Fri, Feb 13
Week 6: Mon, Feb 16
II.3, HW: 1, 2, 3, 4, 5, 8
Wed, Feb 18 Fri, Feb 20
Week 7: Mon, Feb 23
II. 4, HW: 2, 4
II. 5, HW: 1, 3, 10ac
Wed, Feb 25 Fri, Feb 27
Week 8: Mon, Mar 2
III.1, HW: 1, 2, 3
Wed, Mar 4 Fri, Mar 6
Week 9: Mon, Mar 9
III.2, HW: 2, 4, 5, 6, 8
Wed, Mar 11 Fri, Mar 13
Spring Break: Mon, Mar 16
Wed, Mar 18 Fri, Mar 20
Week 10: Mon, Mar 23
III.3, HW: 1, 4, 7
Wed, Mar 25 Fri, Mar 27
Week 11: Mon, Mar 30
III.4, HW: 1, 2, 4, 5a
Wed, Apr 1 Fri, Apr 3
Week 12: Mon, Apr 6
IV.1, HW: 1, 3
Wed, Apr 8 Fri, Apr 10
Week 13: Mon, Apr 13
IV.2, HW: 3
Wed, Apr 15
Fri, Apr 17
Week 14: Mon, Apr 20
IV.3, HW: 2, 6
Wed, Apr 22 Fri, Apr 24
Week 15: Mon, Apr 27
IV.4, HW: 3
Wed, Apr 29 Fri, May 1
Final exam: TBA