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)
   Introduction
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.

2-3
Zermelo's theorem
Problem 14
2-5
More on voting
These problems
2-6
More voting, Discussion of projects
 none

       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.

2-10
Back to game theory
Problems 15,16
2-12

Problem 17
2-14
Start mixed strategies
Problem 18

        Hand in Problems 16 and 17 on Monday.

2-17
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.
2-19
Start von Neumann's theorem    
nothing new, just the problems from Monday.
2-21
Proof of von Neumann's theorem  
Problem 22

          Hand in Problems 19 and 21 on Monday.

2-24
End of von Neumann's theorem and applications    
Problem 23
2-26
General-sum games
test
2-28
Nash bargaining axioms
Problems 24, 25(a)

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

3-03
Solving bargaining games                           
Problem 25b,c        
3-05
Threat games
Problem 25d,e
3-06 (X-hour)



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