Economics 431: Games and Decisions
Meets Mondays and Wednesdays, 12:30 - 1:45, in McClelland 130.
Exercise and review session meets Mondays, 5:30 - 6:30, in McClelland 130.
Professor: Mark Walker.
Office hours: Wednesday 2:15 to 3:00, McClelland 401G
Also by appointment:
Teaching Assistant: Bill Janss
Office hours: Tuesday 2:00 to 3:00, McClelland 401X
Also by appointment:
P. Dutta: Strategies and Games, MIT Press.
You'll also find it helpful to read
Roger McCain's introduction to game theory.
Optional course materials will regularly be made available for
purchase at the Harvill Copy Center, in Room 137 of the Harvill
Building. These will include such things as lecture notes, solutions
to exercises and exams, optional additional exercises, etc. The total
cost of all these optional items, over the course of the semester,
will be less than ten dollars.
I expect you to have an email account and to check it regularly. I'll often
make course announcements by email, and otherwise communicate with everyone in
the class via email. Moreover, you'll find it much easier to communicate with
me or with the TA by email than by phone.
This course is an introduction to decision theory and game theory.
Decision theory is the study of decision making in the presence of
uncertainty. It tells us how to devise a plan or strategy for the
acquisition of information and for what actions to take when new
information is acquired, and how to determine the value of information.
Where decision theory studies decision making by a single decision-maker (an
individual, a firm, a single government, etc.), game theory is concerned with
interaction among multiple decision-makers -- situations in which the
outcome of my own decision depends upon what others do as well as upon what I
do. Game theoretic methods have become central to economic analysis in recent
years. We will use game theory to study bargaining, competition in markets
with only a few large firms, arbitration procedures, contracts between agents
and their "principals," employee compensation arrangements, the value of
reputation, strategic voting, competition among political parties, and other
economic and political subjects.
Exercises, Quizzes, Exams, and Grading:
Regular exercises will be assigned. The exercises will give you
practice and feedback on how you're doing. The exercises will not be
graded, but if you talk about them with the TA or with me, we'll be
glad to tell you how you're doing and to help you with any
difficulties you're having. The TA will hold office hours;
you should take advantage of this opportunity to get help.
There will sometimes be a brief quiz during lecture; the quiz will be
a part of one of the exercises you have been assigned, or will be very
similar to one of the exercises. The quizzes will count as one "unit"
in determining your course grade (see below). Your worst two quiz
grades will be discarded (except that if you choose not to take the
final exam, no quiz grade after the last midterm will be discarded).
Missed quizzes cannot be made up.
There will be two mid-term exams and a comprehensive final exam.
The quizzes are one unit, each mid-term exam is one unit, and the
final exam is two units. Your course grade will be the average of
your best three grades from among those five units. In other
words, your worst two grades will be discarded. (An example:
Quizzes B; Mid-term exams F and B; Final exam C. The F and one C
are discarded, leaving you with two Bs and a C, and your course grade
is therefore a B-. If the Bs and the C are very high ones, your grade
is a B; if all are very low, it might be a C+. But only these three
grades are counted.)
!! There will be no make-up exams !!
( This includes the final exam )
1st Midterm Exam: Wed., February 21.
2nd Midterm Exam: Wed., April 18.
Final Exam: Monday, May 7, 11:00 am.
First Midterm Exam Grade Distribution (after the retake):
Grade Points #Exams (Each of the four problems was worth 20 points.)
A 71-80 12
B 61-70 14
C 51-60 5
D 45-50 1
F 0-44 5
Second Midterm Exam Grade Distribution (after the retake):
Grade Points #Exams (Problems worth 15,20,20,20 points.)
A 65-75 4
B 55-64 11
C 45-54 13
D 35-44 6
F 0-34 2
- The scoring of the quizzes is as follows:
3: Mostly correct
2: Some things correct, some incorrect
1: Mostly incorrect
0: Nothing answered correctly
The following quizzes and quiz solutions are available by clicking on them. The remaining quiz solutions can be found as exercise solutions.
Quiz #1 Solution
Quiz #2 Solution
Quiz #5 Solution
Items At Harvill Copy Center
1. Notes from Lecture 3 (M 1/22)
2. Notes from Lecture 4 (W 1/24)
3. Solutions for Exercise Set #1
4. Solutions for Exercise Set #2
5. Notes from Lecture 8 (W 2/7)
6. Solutions for Exercise Set #3
7. Solutions for Exercise Set #4
8. Notes from Lecture 18 (W 3/21)
9. Notes from Lecture 19 (M 3/26)
10. Notes from Lecture 20 (W 3/28)
11. Notes from Lecture 21 (M 4/2)
12. Solutions for Exercise Set #7
13. Notes from Lecture 23 (M 4/9)
14. "Certainty Monetary Equivalent"
15. "Plotting Your Own VM Utility Function"
16. An Extensive Form Game: Nim
17. Solutions for Exercise Set #8
18. A Simple Poker Game
19. Games of Perfect Information
1. The Prisoners' Dilemma
3. An Oligopoly Game
4. Winner-Take-All Matches in the Lab
- Roger McCain's
Game Theory: An Introductory Sketch, a very nicely done
introduction to most of the essential ideas in game theory.
- Paul Walker's excellent
Chronology of Game Theory and bibliographic notes.
- Michael Carter's compendium of
books about game theory,
including books that apply game theory to economics, political science, law,
biology, evolution, and decision-making in business.
- Sylvia Nasar's
NY Times article about John Nash
when he was awarded the Nobel Prize for Economics. A fascinating,
emotional story. Her subsequent book about Nash,
A Beautiful Mind,
is also excellent.
interactive repeated Prisoners' Dilemma game from Serendip, the
nom de chippe of a group of people at Bryn Mawr College.
- How long will it take you to beat the computer? Here's a very nice
where you can play and read about the game "Hex," also called "Nash." It's the
game invented by John Nash in 1948 when he was a graduate student in
Princeton's math department, at about the same time as he thought of the idea
now known as Nash equilibrium.
describes how the game became the rage in Princeton's math department.
David Levine's Game Theory and Economics Page, which contains
(among other things) a
, a neat little tool that allows you to enter the payoffs of a two-person
zero-sum game, and then it calculates an equilibrium mixed strategy for the
Column player. Transpose the payoffs to get the Row player's mixed strategy.
- The Monty Hall Problem: A huge number of websites ... just do a search for
"Monty Hall" and you'll get lots of hits. Some of the best are
John Upper's demo (with great sound effects!) for his Queen's University
philosophy course (click on "The Demo"; the page also has some interesting
discussion of the problem);
David Little's also cool demo and explanation for his UC San Diego math course in
cryptography (this one shows you the total wins and losses by everyone who's
ever played the demo, using either the Stay strategy or the Switch strategy);
a simulation, also by David Little, which allows you to simulate a large
number of plays, with either strategy, and under two alternative rules for
Monty to follow; and
both a demo and a simulation provided by the Shodor Education Foundation
(the simulation allows for an arbitrary number of doors, which changes the
probabilities in a revealing way).
Mark Walker's Home Page