Game Theory Syllabus: MATH 3590

 

Game Theory: MATH 3590, 3 credit hours

 

Prerequisites: Grade of C or above in MATH 2040 or MATH 2450

 

Catalog Description: Game theory models will be discussed from a humanities-based, decision-sciences perspective.  Topics will include strategic, matrix and sequential games, optimization, Nash equilibria and strategies.  Applications will include economic and strategic (military) models, the Prisoner’s Dilema, Cournot Duopoly, bargaining and auctions.

 

Grading: The course will be largely project-based with homework sets (every two weeks) and an in-class midterm exam.  The math career simulation project (30% each), homework & quizzes (10%), the midterm (30%) and the final project (30%) will comprise a student’s course grade.  Help will be available for students as they devise their projects, both with selecting appropriate real-world problems and with setting up the games mathematically.  Creativity and research beyond the scope of the texts/lecture are encouraged and will be highly rewarded.  For some projects, teams will be formed.  Presentation to the class of project results is considered part of the project grade.  The most interesting class days will be those in which students demonstrate their creativity and game theoretic prowess.

 

Course Objectives: After completion of the course, students will be able to:

 

Methods of Instruction: The methods of instruction are determined by the instructor; however, the instructor is expected to use a variety of methods.  These methods may include, but are not limited to lecture, problem-solving sessions, discussion, group projects, question and answer sessions, computer or calculator-based explorations, and student presentations.  In addition, timely feedback from tests, quizzes, and projects is expected.

 

Methods of Evaluation: Formative assessment may be informal (self-evaluation, peer-evaluation, and instructor evaluation) or formal (tests, quizzes, projects, and daily grades).  Summative assessment will be in the form of a final examination.  Students will be encouraged to assess and monitor their own problem-solving process to determine when an error has been made or a new strategy should be used.

 

Course Content: A tentative schedule is shown below.

 

Week(s)

Topics

Approximate Meeting(s)

1 - 2

Functions & Optimization

4

3

Lagrange Optimization

2

4

Uncertainty & Decision Making

2

5 - 7

Matrix Games & Strategic Form Games

6

8-9

Sequential Games, Game Trees and Equilibria

4

10

Beliefs, Strategies and Consistency

2

11

Auctions

2

12

Bargaining

2

13 - 14

The Core, Nash Solutions & Shapley Values

4

 

Knowledge Base:

 

1.      Required Text: Straffin, P. D., Game Theory and Strategy, The Mathematical Association of America, 2002.

 

2.      Optional Texts: Aliprantis, C. D. & Chakrabarti S. K., Games and Decision Making, Oxford University Press, 2000.  Dixit, A. K. & Nalebuff, B. J., Thinking Strategically: The Competitive Edge in Business, Politics and Everyday Life, W. W. Norton & Co., 1991.

 

3.      Library Resources: Selected titles are listed below.

·        Women and Science Celebrating Achievements Charting Challenges (National Science Foundation, 1997)

·        Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (Janet Trentacosta & J. Kenney, Eds., NCTM, 1997)

·        She Does Math! (Marla Parker, Ed., The Mathematical Association of America, 1995)

 

4.  Web-Based Resources:   

·        Association for Women in Mathematics - www.awm-math.org

·        Texas Instruments - www.education.ti.com

·        Eric Weisstein’s World of Mathematics (Encyclopedia of Mathematics) - mathworld.wolfram.com

·        TEAMS Mathematics Resources - teams.lacoe.edu/documentation/places/math.html

·        Math Nerds – www.mathnerds.com

·        SOS Mathematics – www.sosmath.com

·        Intermath – www.intermath-uga.gatech.edu/

·        Women in Mathematics - www.agnesscott.edu/lriddle/women/women.htm

 

5.      Technology Resources:     

·        A graphing calculator such as a TI-83 / TI-84 or TI-89 is required.

·        Software: Microsoft Excel.

·        Web-Resources: Course Blog Site www.ctle.ngcsu.edu/rsinn and Web Site radar.ngcsu.edu/rsinn/courses/3590.  Students should be able to access all resources and contribute to the blog.

 

General Expectations: The student is expected to abide by the university's attendance policy and integrity code.  Other expectations may be given by the instructor.

 

Academic Integrity:  Students are expected to adhere to the Academic Integrity Policy for the University:  "On my honor, I will not lie, cheat, steal, plagiarize, evade the truth or tolerate those who do."  Violations of the Academic Integrity Policy will be reported to the Academic Integrity Council in an incident report.  Please refer the to NGCSU’s Undergraduate Bulletin for additional details.

 

Accommodation for Students with Disabilities:  North Georgia College & State University is committed to equal access to its programs, services and activities for people with disabilities.  If you believe that you have a disability requiring an accommodation, reasonable prior notice needs to be given to the instructor and the Office of Student Disability Resources.  In this case, contact Elizabeth McIntosh, Coordinator, Student Disability Resources at 122 Barnes Hall, 706-867-2782, or via email: emcintosh@ngcsu.edu.