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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.

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)

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

1-22	More population modeling	Problem 7
1-23	Tournaments Introduction
1-24	Transitive tournaments	Problems 8,9,10

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