course information


    Mathematics 36               Winter 2003         Tentative Syllabus

 Date             Topics                                                                                 Homework
1-6 Population models Read Chapter 1 and do:  Problem 1
1-8    Interacting populations p. 33:  8, 9  and  Problems 2,3.   Reading: Chapter 3
1-10    Linearizations, classifying equilibria Problems 4,5.   Optional reading for the week: Chapters 3 and 4 of Olinick (on Baker reserve)

  Hand in problem 3 on Monday the 13th.
1-13 Voting theory (Guest lecturer)
Problems a,b,c,d  and For All Practical Purposes, p.186: 1a,b,c, and one part of d.
Reading: Chapter 9 of For All Practical Purposes and chapter 6 of Olinick.
1-15    Voting axioms For All Practical Purposes, p.187: 2,3;  Olinick, p. 192: 9, and p. 193: 19(The voting mechanism, i.e. the function from the set of profiles to group rankings, that you construct does not need to be "reasonable";  and Problem 6.
Handout(Voting Axioms)
1-17    Proof of Arrow's theorem These Problems

    Problems to be handed in on Wednesday, the 22nd: Problems a,b,c,d ,   Problem 6  and  number 19, page 193 of Olinick.
1-22 More population modeling Problem 7
1-23 Tournaments  Introduction 
1-24 Transitive tournaments Problems 8,9,10

    Due Monday the 27th or Wednesday the 29th: Problems 8 and 10
1-27 Consistency of tournaments Problems 11,12  and: How many transitive and cyclic triples does this tournament (which is also on p. 83 of Roberts) have?
1-29 End tournaments, start games
the test
1-31 Values of games
Problem 13

       Hand in Problem 13 on Monday.

Zermelo's theorem
Problem 14
More on voting
These problems
More voting, Discussion of projects

       Due Monday the 10th: 14(a) and one part of 14(b), i.e. either address the case where m and n are both even, or when m is even and n odd, or when m=n=3.  Also, either 1. or 2. of These problems.

Back to game theory
Problems 15,16

Problem 17
Start mixed strategies
Problem 18

        Hand in Problems 16 and 17 on Monday.

Mixed strategies                                                                                       
Problems 19, 20 and 21  Wednesday's class should be helpful for 20 and 21, but you might start on these before it.  There is now a Game theory book on reserve by Binmore.  Much of what we've done is in chapter 1, and chapter 6 discusses mixed strategies.
Start von Neumann's theorem    
nothing new, just the problems from Monday.
Proof of von Neumann's theorem  
Problem 22

          Hand in Problems 19 and 21 on Monday.

End of von Neumann's theorem and applications    
Problem 23
General-sum games
Nash bargaining axioms
Problems 24, 25(a)

           Nothing to hand in on Monday.  Last assignment due on Friday, the 7th.

Solving bargaining games                           
Problem 25b,c        
Threat games
Problem 25d,e
3-06 (X-hour)

        Hand in (under my office door, 312 Bradley) problem 25 anytime Friday.