Math 480 Games and Their Mathematical Models 
Fall, 2000
last revised 10-16-00
W 1300-1450 SH 128 
M 1400-1450 Art 25

Final Examination:Available after Friday 12-8 at 3 pm. 
Due by Thursday 12-21by 5 pm.

• Course Description
• Class Summaries
• Course Assignments: Text Problem lists
• Want to find out what your learning style is? Here are two interesting learning styles inventories on the web: (1) NC State  (2)  Diablo Valley College .
• Game Theory and Mathematical Economics web sites for surfing.

Description: The mathematical theory of games provides a conceptual model for many social, political, and economic contexts. This course will explore several different models for games with their applications both informally and with mathematical rigor. 

Texts: (required)

• Game Theory and Strategy (New Mathematical Library, No 36) by Philip D. Straffin Paperback  (November 1993) Mathematical Ass'n of America
• Game Theory : A Nontechnical Introduction by Morton D. Davis Paperback (July 1997) Dover Pub'ns.

• SCOPE:This course will deal with the theory and application of game theory. The topics covered (listed in greater detail below) will deal with noncooperative and cooperative games involving two and more players involving several solution concepts. Relevant readings will be primarily in Chapters 1-3,7,9-12,14,16,19,21,23,25-29,31, and 33 of Straffin will correlative readings in Davis. Application chapters will be selected from the Straffin. Supplementary notes and text will be provided as appropriate.
• TESTS AND ASSIGNMENTS:  There will be two tests in this course, a midterm and a final examination.
• The Midterm Exam will be announced at least one week in advance.
• THE FINAL EXAMINATION WILL BE SELF SCHEDULED.
• The final exam will be comprehensive, covering the entire semester.
• Homework assignments are made regularly and should be passed in on the due date. All homework is due by 5 pm of the assigned date. In general late homework will have its grade lowered by 20% for tardiness.
• Homework is graded at 5 points per problem (5=correct, 4 or 3= some minor errors, 2 or 1 = some major errors, 0 = no essential progress) with an opportunity to submit corrections for at most 2 additional points. Redone work should be returned for grading promptly with the original graded work. Homework points will be used to determine 40 % of the final grade.
• Class Presentations: Each student must give at least one class presentation of a game theory application (or theory). These may be done individually or with a partner. (If done with a partner at least two presentations are required).
• Additional presentations (up to a total of 3) will be elective for each student.
• Additional elective presentations will be used for an increased percent of  the final grade based on presentations, balanced by  a reduction in the percent contributed to the final grade by the final examination.
• Presentations will be graded out of 5. If only one presentation is made, the presentation will determine 5% of the final grade.
*** DAILY ATTENDANCE SHOULD BE A HABIT! ***
• GRADES: Final grades will be determined taking into consideration the quality of work done in the course as evidenced primarily from the accumulation of points from tests and  assignments. In determining the balnce between these points the following balancing percentages will be applied.

Midterm exam	15%
Presentation(s)	5-15%
Homework	50%
Final exam	20-30%
TOTAL	100%

 

Notice that as little as 35% , and at most 45% of your grade is from examinations, so regular participation is essential to forming a good foundation for your grades as well as your learning.
Missing more than 6 hours of class time may lower your final grade for poor participation.

** See the course schedule for the dates related to the following:
No drops will be allowed without "serious and compelling reasons" and a fee.
No drops will be allowed.
Students wishing to be graded with either CR or NC should make this request to the Adm & Rec office in writing or by using the web registration procedures. See the fall course list for a full list of relevant days. 

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• Technology: The computer or a graphing calculator can be used for many problems. We may use X(PLORE), Matrix, GAMBIT, or Winarc.
• A version of X(PLORE) is available at the bookstore for  MAC based PC's along with the PC version we will use.Windows and DOS versions of X(PLORE) are also available online...X(PLORE) for Windows.
• Matrix is freeware for PC's available from the Math Archives Web Site. or the zipped file may be downloaded directly.
• Winarc, a collection of game subprograms,  currently including Life, Krypto, Boxes, Hex, Rubik, Mazes,  Pegs, Bishops, the Loyd 15 puzzle, and Spaceship. is freeware and may be downloaded from Rick Parris's website or directly from this link for Winarc .
• GAMBIT can be used to solve games in normal or extensive form.
• Graphing Calculators: Graphing calculators are welcome and highly recommended. We may use the HP48G for some in-class work though most graphing calculators will be able to do much of this work. HP48G's will be available for students to borrow for the term through me by arrangement with the Math department. Supplementary materials will be distributed if needed. If you would like to purchase one or have one already, let me know. Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class.

Back to HSU Math. Department :}

• Definitions of a game.
• Extensive Form
• Normal Form
• Two Person Zero Sum Games
• Normal Form
• Mixed strategies
• Key Probability and Statistics Concepts [from Finite Mathematics Applied to the Real World]
• Mini-Max Solutions
• Computational aspects [from Finite Mathematics Applied to the Real World]
• Linear Programming using the Simplex Method On-line tutorial for Section 4.3 of
•  On-Line Game Theory Chapter Summary
• On-Line Game Theory Utility (Does everything, including solving games and  playing against you!)
• Utility Theory
• What and why?
• Lotteries.
• Commodity bundles.
• Two Person General Sum Games
• Bimatrix Games (Non-cooperative equilibria)
• Bargaining
• Threats
• n- Person games
• Noncooperative games
• Cooperatives games
• Solution concepts
• - Core
• - Stable sets.
• Other topics as time permits
• Power indices
• Bargaining Sets
• Games without side payments.
• Multistage games
• Games with a continuum of player (nonatomic games)

Last updated: 8/17/00