**Seminar on Algorithmic Game Theory**

**Instructor: ** Christos
H. Papadimitriou

Soda
689, christos@cs,
(510) 642-1559

**Office Hours: **Wednesday
and Thursday 5-6, and by appointment

**Meets:** Tuesdays
3:30 – 6:30pm, Soda 405. From Sept 27 on, we shall meet at
Soda 306.

**What: **A
graduate seminar about the computational aspects of game theory. The
recommended text * Algorithmic
Game Theory* by
Nisan, Roughgarden, Tardos, and V. Vazirani will
be useful for large parts of the class.

The course will be offered concurrently/jointly with a course at MIT taught by Costis Daskalakis, see the last version of that course to get an idea of the material that we will cover. The lectures will not be synchronized (MIT starts later than us), but the material will overlap a lot and the notes/lecture slides will be largely the same. In other words, you can ignore the MIT mirror, but you may want to be aware of it.

**Course Requirements:**

·
*Attendance and class
participation.*

· Weekly problems.

· Scribe once, team of two.

· In addition, student teams will work on a project, surveying the research frontiers in a topic, ideally pushing the frontiers a little. Applying game theory ideas to other fields in a novel way is also a possibility.

* Important rule about
homeworks:* Collaboration
and consultation of sources is allowed and encouraged. It is,
of course, explicitly acknowledged in the manner familiar from all
scholarly work.

**News**

Have you filled the course’s (mailed it to me?)

Here are my notes from Lecture 1, and scribe notes. Remember the problems due next week.

Here are scribe notes for Lecture 2.

For Lecture 3, you may want to look at Chapter 2 of the AGT book, and these two papers.

* New
Homework! *(Due:
Sept 27) The project is a part of the class requirements. The project
should be a research-like experience (immerse yourself in a research
problem until you hit the frontiers, and in a good semester advance
them). You should think of it as two weeks worth of serious work
(probably spread over the last six weeks of the semester). Another
possibility is a novel application of game theory ideas to your own
research world. You can team up with one or two colleagues. Your
immediate task is to spend a few hours looking at the various
chapters of the AGT book, other books you may want to skim, at
abstracts in the conferences EC, WINE, and SAGT, and anywhere else
you choose on the web or the library, and write a page about your
current thoughts. This should include your top two-three ideas for a
project (unless you have fully decided), any initial contacts with
others to form a team, and any other relevant information that
convinces me you have started to think about it seriously.

Recall the lawyers’ game from the lecture. There are n blue and n red players (n is odd) playing a separable network game with two strategies each, with payoffs at most 2, say. They are to be represented by two lawyers, R and B. The action sets of each lawyer is the union of the action sets of his n customers. The intention is that the network game is simulated. To avoid “injustice” in which a client gets more probability mass than its share, the lawyers play on the side a generalized RPS game (with n implements). Implement I beats implement i+1 (mod n), and in all other cases we have a tie. The stakes of this game are huge: M.

A. Describe the payoffs of this game.

B. Show that at any Nash equilibrium, the sum of the probabilities of the two actions of each client satisfies | sum – 1/n | = O(n^2/M).

Scribe notes for Lecture 3.

Scribe notes for Lecture 4.

Scribe notes for Lecture 5.

Scribe notes for Lecture 6.

* New
Homework! *(Due:
Oct 18) A: Suppose that a consumer has utility function
that is piecewise linear of the form U(x) = u_1(x_1) +…+u_n(x_n),
where each u_i is of the form “if x < c then ax otherwise ac +
b(x-c), where a > b. What is the demand of this consumer
when her budget is B?

B: Prove that the CES utility for rho < 1 and not zero is concave.

C: Write a page about your project (you have decided by now), what you have done so far, and what you plan to do by Thanksgiving (that’s when they are due). Remember, you should expect to spend roughly two weeks on it. One per team.

Scribe notes for Lecture 7.

Scribe notes for Lecture 8.

Scribe notes for Lecture 9.

Scribe notes for Lecture 10.

Scribe notes for Lecture 11.

There will be no lecture November 15. Instead, work on your projects and make an appointment to discuss them with me, Thursday Nov 17, any time.

my notes for Lectures 12 and 13 (November 22 and 29).

Important!
The project presentations will **not** be Tue at 4 (no room
available).

**It
will be Wednesday 3-6 at Soda 380. See you there!**