The activities are an opportunity for you to further explore the various aspects of the subjects we're covering, with more flexibility than the usual problem sets offer. I will be suggesting activities throughout the semester. You do not have to do all of them -- pick and choose among those that sound interesting to you, or come up with your own ideas!

I will be adding to this page as I have ideas. Feel free to suggest any ideas to me!

Activity 1
Model a real-life situation with a 2x2 (or 2x3, or 3x3) ordinal game. Analyze the game, with or without the theory of moves as seems appropriate to the situation. Look for dominant strategies, Nash or non-myopic equilibria. Finally, discuss how well your model matches reality.
Due 3/7.

Activity 2
Design a problem for an exam, and provide the solution.
Due 3/30 for Exam 2 problems, 4/27 for Exam 3 problems, 5/2 for Final problems

Activity 3
Do a theory of moves analysis on a 2x2 or 3x3 game. Make up the game that represents the initial situation (you can either just make up the table or for additional points, start with a ``story'', like in the first activity). Do not use the Prisoner's Dilemma or Chicken. Then do a complete analysis of where the theory of moves takes you -- for each starting position, is it a non-myopic equilibrium? Does either player have a dominant strategy in their initial choice?
Due 3/30

Activity 4
Attend one of the science talks this term (Puzzles in Science, for instance) and write a discussion/reaction.

Activity 5
Investigate the voting method used in Cambridge MA, and write a brief description of how the method works,giving your own examples. Consult MIT's interactive website .

Activity 6
Research what experts believe about actual fairness and relevance of various voting methods. One option: does anybody recommend we should replace our current method of electing the president with some other method -- Borda for instance? Why? Another option: look into methods we haven't learned about. The method used in Cambridge is referred to above; there is also approval voting, Charles Dodgson (Lewis Carroll) devised a method, and there are many others. Activity 7
Find an example of a real-life situation (other than those mentioned in the book) where a voting method other than plurality is used. Describe it in detail, and either give an example of the results of a specific election/vote or make one up to demonstrate how it works (or both).

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu