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

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, Aug 25
I.1, HW: 1, 2, 4, (and try 6 too)
I.2, HW: 2, 3, 4, 5, 7a
Wed, Aug 27 Fri, Aug 29
Week 2: Mon, Sep 1 (no meeting)
Labor Day
Wed, Sep 3
I.3, HW: 1, 2, 3, 5
I.4, HW: 1, 2, 3, 4, 5, 10
Fri, Sep 5
Week 3: Mon, Sep 8
I.5, HW: 1abcd, 2abc
Wed, Sep 10 Fri, Sep 12
Week 4: Mon, Sep 15
II.1, HW: 1, 3
Wed, Sep 17 Fri, Sep 19
Week 5: Mon, Sep 22
II.2, HW: 1, 3, 4, 5, 6, 7, 8
Wed, Sep 24 Fri, Sep 26
Week 6: Mon, Sep 29
II.3, HW: 1, 2, 3, 4, 5, 8
Wed, Oct 1 Fri, Oct 3
Week 7: Mon, Oct 6
II. 4, HW: 2, 4
II. 5, HW: 1, 3, 10ac
Wed, Oct 8 Fri, Oct 10
Week 8: Mon, Oct 13 (no meeting)
October Break
Wed, Oct 15 Fri, Oct 17
Week 9: Mon, Oct 20 Wed, Oct 22 Fri, Oct 24
Week 10: Mon, Oct 27
III.1, HW: 1, 2, 3
Wed, Oct 29 Fri, Oct 31
Week 11: Mon, Nov 3
III.2, HW: 2, 4, 5, 6, 8
Wed, Nov 5 Fri, Nov 7
Week 12: Mon, Nov 10
III.3, HW: 1, 4, 7
Wed, Nov 12 Fri, Nov 14
Week 13: Mon, Nov 17
Homework for the rest of the semester:
III.4, HW: 1, 2, 4, 5a
IV.1, HW: 1, 3
IV.2, HW: 3
IV.3, HW: 2, 6
IV.4, HW: 3
Wed, Nov 19 Fri, Nov 21
Week 14: Mon, Nov 24 Wed, Nov 26
Thanksgiving Vacation
Fri, Nov 28
Thanksgiving Vacation
Week 15: Mon, Dec 1 Wed, Dec 3 Fri, Dec 5
Week 16: Mon, Dec 8 Wed, Dec 10 Fri, Dec 12
Final exam: TBA