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).

do some "applications to economics".

students in mathematics and mathematical statistics, and graduate students in computer

science and economics. Faculty are also of course welcome.

For a sense of

(Part I there deals with "combinatorial game theory", which is somewhat different and will

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.

- 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?

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.

number of students) presentations of papers.

Last modified: Fri Nov 22 11:13:34 MET DST 2002