Econ 4010 Syllabus Fall 2015
Current Version August 19 2015
Instructor: Maxim Engers Office: Monroe Hall 230
Phone: 924-3130. Electronic Mail: maxim@virginia.edu Office Hours: Tues 3.30 - 5 pm
TA: Brett Lissenden Electronic Mail: [email protected]du Office Hours TBA
Class Webpage: Available through Collab
Course Goal: To provide a challenging introduction to the most important ideas in game
theory, with an emphasis on applications to microeconomics. Game theory (which is
really the theory of multiperson decisions) is a branch of mathematics that is
indispensable to modern economic theory and has useful applications to areas as
diverse as biology, politics, and corporate strategy to name a few. We will emphasize
applications to economics, and introduce some key ideas in mechanism design, which
uses game theory to answer questions like: “What is the most advantageous way for
someone to sell something when the seller doesn’t know how much the potential buyers
are willing to pay?”
Note: If you are not very comfortable with calculus or you do not enjoy solving
problems then this course is definitely not for you. Students have told me that this class
is significantly more difficult than the typical economics class. If you prefer not to take
very challenging classes then taking some other class would be a much better choice.
Accommodations: Any student who feels that he or she may need to discuss individual
accommodations, please make an appointment to see me as soon as possible. If you are
entitled to receive extra time on tests, you should let me know as soon as possible at the
beginning of the semester so that I can make the necessary arrangements.
Use of Class Material from Past Semesters, Answer Keys or Solutions Manuals: I expect
that students will not use exams, problem sets or other materials from previous semesters
of this course to study for the exams or to complete assignments. In this class, using
materials from past semesters, or using answer keys, or solutions manuals is considered a
violation of the UVA honor code.
Text: The following book is required:
Martin J. Osborne: An Introduction to Game Theory, Oxford, New York, 2003.
One of the main advantages of the text is that it has many exercises and the author has
made the answers to many of them are available on the web (follow a link at
https://www.economics.utoronto.ca/osborne/igt/index.html
Grading: There will be a midterm and a final exam. Depending on available grading
assistance, between three and six problem sets will be required and they total 20% of
your grade. The midterm counts 35% and the final 45%. Problem sets handed in less
than a day late will be penalized 50%. More than a day late they will not be accepted.
Acceptable reasons for missing an exam are incapacitating illness, participation in a
university-sponsored intercollegiate competition, family emergency, or major religious
holidays. If you do miss the midterm you should inform me of your excuse within one
week of the exam. No make-up tests will be given, but if you have an acceptable excuse
your other scores will be scaled up proportionately. (An adjustment may be made if the
class performance indicates that the test was significantly harder or easier than the other
requirements.) If your excuse is unacceptable your grade will be similarly adjusted, but
you will be subject to a 25 % penalty. Examples of unacceptable excuses are
oversleeping, losing your notes, or having had rehearsals the night before the test.
The midterm will be given in class on October 8.
Final Exam: Because I plan to be out of town during the exam period you will not be able
to reschedule your exam. If you are unable to take the final exam as scheduled at 9 am
on Dec 17 you should drop this class.
Punctuality: I expect you to be on time for classes. Late arrival disrupts everyone’s
concentration. Very occasionally, because of unusual circumstances, you may be late. If
you are late you must send me, by the end of the working day, an email message
explaining why you were late and outlining the steps you are taking to make sure that you
will be not be late again. If you don’t, your final grade can be penalized up to three
percentage points for each infraction
Other Sources: Students wanting to try other approaches to the material may find the
following references useful: The books are listed in increasing order of difficulty. The
first two are at a more elementary level than our text, the last two are at a more advanced
level than our text, and the middle book is at about the same level as our text.
Avinash K, Dixit and Barry Nalebuff: Thinking Strategically, Norton 1991.
(When the authors started to revise the book they ended up substantially rewriting it as
The Art of Strategy: Norton 2008)
Avinash K, Dixit and Susan Skeath: Games of Strategy, Norton 2001
Prajit K. Dutta: Strategies and Games, Cambridge MA: MIT Press, 2001
Robert Gibbons: Game Theory for Applied Economists, Princeton 1992
Drew Fudenberg and Jean Tirole: Game Theory, MIT 1991
An elementary book that applies game theory to business decisions is:
Adam Brandenburger and Barry Nalebuff: Co-opetition, Doubleday, 1996
To do well in 4010 it is more important to concentrate on the topics we cover in
class than to read everything in the textbook. Your class notes should be the best guide
for studying for the exams. If you miss a class you are responsible for getting the class
notes from someone who was present.
Prerequisites: A basic knowledge of calculus and of fundamental concepts of
probability is needed for this course. In particular you need to know how to use calculus
to solve maximization problems like the following
Find the positive number x that makes the value of the function f(x) = x
1/x
as big as
possible.
You should be familiar with the formula for conditional probability for one event A given
another event B. You should know what a continuous random variable is and you should
know what a probability distribution function and a probability density function are. As a
check you should be able to answer the following
If X is uniformly distributed between 2 and 10,
(a) find the probability distribution function and the probability density function for
X
(b) find the expected value of X
3
The bad news is that we will be beginning the semester with a test, to be given
during the first meeting of discussion section. The test is required: If you are absent you
will be dropped from the class. The good news is that your grade will not count towards
your final grade in the course. The exam is designed for your benefit: Its purpose is to
tell you whether you have the background in, and facility with, the mathematics and
statistics that are necessary for success in Econ 4010.
To prepare for the test you may want to spend a few hours reviewing selected
topics in mathematics and statistics. In mathematics, you should review differentiation of
functions, including power, exponential, and log functions; differentiation of sums,
products, and quotients of functions, and of composite functions (via the chain rule).
You should also review the use of calculus to determine maxima and minima (including
first- and second-order conditions).
In statistics you should review basic ideas of probability including continuous and
discrete random variables, probability density functions, and (cumulative) distribution
functions. You should check that you know how to calculate the expectation of a
function of a random variable
If you do poorly on the test, I will not force you to drop the class, but I would
strongly advise you against continuing. It would be better to change to a class that does
not use as much math or probability, or wait and improve your math skills before again
trying 4010.
Trying to add into 4010?
If you are trying to add into Econ 4010 from the wait list it is important for you to
come to all classes and to do as well as you can on the background test. I will be
deciding which students to add on the basis of these criteria because I believe that they
best indicate which students will benefit the most from taking the class. Because of the
number of students who want to add in there will likely be some more challenging
questions on the test. You can’t really prepare for these but just try to be alert and be in
command of your knowledge of calculus, basic probability and intermediate micro.
Reading Guide
The table below gives a rough outline of the topics to be covered and when we plan to
cover them: we may proceed faster or slower than this table indicates. The number in
bold type refers to the chapter of the textbook that deals with the material. Sometimes we
will deal with a topic in much greater depth than the textbook does: these topics are
followed by an asterisk *
Tuesday
Thursday
Aug 25 Introduction
Aug 27 2 Static (Strategic Form) Games
Sep 1 2 Auctions, and Dominance
Sep 3 2 Nash Equilibrium
Sep 8 3 Cournot and Bertrand
Sep 10 4 Mixed Strategies
Sep 15 5 Dynamic Games and Backward Induction
Sep 17 5 Subgame Perfect Equilibrium
Sep 22 5 14 Finitely Repeated Games
Sep 24 Infinitely Repeated games
Sep 29 16 Bargaining *
Oct 1 16 Bargaining *
Oct 6 Reading Day
Oct 8 MIDTERM EXAM
Oct 13 Go over midterm
Oct 15 Static Games of Incomplete Information
Oct 20 Cournot with Private Costs
Oct 22 9 Private Value Auctions
Oct 27 Auction Equilibrium *
Oct 29 9 Revenue Equivalence *
Nov 3 Reserve Prices
Nov 5 9 Optimal Auctions *
Nov 10 The Revelation Principle and Mechanism
Design*
Nov 12 9 Common Value Auctions *
Nov 17 10 Dynamic Games of Incomplete
Information *
Nov 19 10 Perfect Bayesian Equilibrium*
Nov 24 10 Signaling games *
Dec 1 10 Refinement in Signaling Games
Nov 26 Thanksgiving
Dec 3 10 Signaling in labor markets*
Dec 8 10 Signaling in labor markets*
DEC 17: 9 A.M. FINAL EXAM