Classical Game Theory (5 points)
Here
is the schedule for the course. The first day is Wednesday, February 5
at 8:15 in MD 9.
Lecture notes for course.
First lecture
(written by Pierre Hyvernat)
Second lecture
(written by Pierre Hyvernat)
Third lecture
(written by Mats Kvarnström)
Fourth lecture
(written by Mats Kvarnström)
Fifth lecture
(written by Johanna Pejlare)
Sixth lecture
(written by Johanna Pejlare)
Seventh lecture
(written by Peter Hegarty)
Eighth lecture
(written by Peter Hegarty)
Ninth lecture
(written by Devdatt Dubhashi)
Tenth lecture
(written by Fredrik Engström)
Eleventh lecture
(written by Fredrik Engström)
Twelth lecture
(written by Fredrik Altenstedt)
Thirteenth
lecture
(written by Fredrik Altenstedt)
Fourteenth
lecture
(written by Sverker Lundin)
Fifteenth
lecture
(written by Sverker Lundin)
Homeworks are following.
Assignment 1
(It would be nice to get this Friday, the 21st.)
Assignment 2
(Due March 14).
Assignment 3
(Due April 2).
COURSE GOAL:
Give an introduction to classical
game theory and also
do some "applications
to economics".
TIME:
This course will run for the third "reading period" and part or most of the
fourth.
INTENDED AUDIENCE:
This course is intended for graduate and
undergraduate
students in mathematics and mathematical statistics,
and graduate students in
computer
science and economics. Faculty are also of course welcome.
SOME COMMENTS:
This course will give an introduction to
classical game theory.
For a
sense of some of
the topics that we plan to cover, go
here
and look at Parts II and III
there.
(Part I there deals with "combinatorial
game theory", which is somewhat different and will
NOT
be covered in this course).
ONE MORE COMMENT:
While game theory is a very interesting subject in itself, the
implications for economics have also been very important.
This can for example be seen
in the fact that Harsanyi, Nash and
Selten shared the Nobel prize in economics in 1994.
PRELIMINARY TOPICS TO BE COVERED:
Part I
- 2 person-zero-sum games. Here the value of a game and optimal
strategies are
introduced,
von
Neumann's
minimax theorem will be proved using
the separating
hyperplane
theorem (which will also be proved)
and a number of other things for 2 person-zero-sum
games
will be covered.
- Some topics on infinite games.
- n-person noncooperative games and the fundamental concept
of a Nash equilibrium.
We will give the proof of
Nash's theorem that all finite games have such
equilibria.
This
is based on the Brouwer fixed point theorem, which
in turn will be given a
combinatorial proof.
- Correlated equilibria.
- Games with imperfect information and Bayesian equilibria.
- Repeated games with one-sided imperfect information
(the complete solution here
will turn out to be given
in terms of the `concavification' of a particular related
function).
Part II
The second part of the course will concern
(very loosely speaking perhaps) some
"applications to economics".
- The Cournot Model of Duopoly (an example where the
famous "prisoner's dilemma" arises
when there are two firms in a market).
- Nash's axiomatic solution to the bargaining problem with applications
to 2 person nonzero sum
games
with contracts and transferable utility.
- Rubinstein's alternating bargaining game
and its relationship to Nash's solution.
(This will demonstrate why a person
in a rush to close a deal will end up with less.)
- Optimal design of auctions.
[Here a key object of study will be a so-called
mechanism design
where games are constructed in order
to have participants behave in some optimal way
for the designer.]
- maybe more?
Prerequisites: Undergraduate analysis, elementary
probability and linear algebra.
Course literature:
There will be no official book for the course but
rather everything will
be based on course notes. Nonetheless,
I believe that the following three items below will
cover most of what we will be doing in the course.
- For lots on zero sum games and some things on general sum games,
see Parts II and III and
appendix 2 in
the link given above (these are notes by T. Ferguson at UCLA).
- Game theory by R. Myerson is an excellent text and relatively
cheap, go to amazon.com.
- Myerson, Roger B. Optimal auction design. Mathematical Operations
Research, Volume 6
(1981), 58--73.
This is an excellent paper on constructing optimal auctions.
Some other recommended books (among very many others)
which one could look at are
- Game theory by G. Owen and
- Fun and games by K. Binmore.
Examination Form:
There will be homeworks, a final oral exam and perhaps
(depending on the
number of students) presentations of papers.
Kursexaminator: Jeff Steif (steif@math.chalmers.se)
Last modified: Fri Nov 22 11:13:34 MET DST 2002