**Seminar on
Algorithmic Game Theory**

**Instructor: ** Christos
H. Papadimitriou

Soda 389, christos@cs,
(510) 642-1559

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

**Meets:** Tuesdays 10-1, Soda 310.

**Course Format: **Lectures by the instructor and other participants.

**Book: ** ** Algorithmic
Game Theory** by Nisan, Roughgarden, Tardos, and V. Vazirani
. We’ll read much of the book, but also
papers that go beyond its coverage.

**Course Requirements:**

- Attendance and class
participation.
- 2-3 problem sets.
- Teams of 2 or occasionally 3
participants will present a lecture, most often the material in one
chapter of the book. This will
start happening soon, so part of the requirement is to be prepared early
for a presentation.
- In addition, student teams will
work on a project, surveying the research frontiers in a topic, ideally
pushing the frontiers a little.

**Course Description**

**News and Handouts**

Have you filled the course’s questionnaire?

*First
Homework, due February 3:*

1.
Read this 1951
paper by Julia Robinson. Write a
short exposition, explaining the proof and focusing on this question: What is the convergence rate, ε as a
function of t? Improving this is an
open problem. Do you think it can be
done? Or could there be a lower bound?

2.
Read the
abstracts of the chapters in the book, and select two or three as initial
indications of the ones you would like to present.

** Reading **for the first three meetings: Chapters 1 and 2 of the book. Here is the full proof of the complexity
result for Nash, here is a simplified
exposition.

**Meetings**

Tue
Jan 20: Seminar inauguration,
administrivia, Nash equilibria.

Tue
Jan 27: Review first lecture’s
material. Nash’s proof
and complexity of Nash equilibria.

Feb
3: Complexity and approximation of mixed
Nash equilibria, correlated equilibria,
extensive form games.

Feb.
10: Extensive form games (selections
from Chapter 3). Also: Costis Daskalakis on symmetry in games; here are his slides.

Feb
17: Learning in games (Chapter 4). Presented by Isabelle,
Jake, and Milos.

Feb
24: General equilibrium theory, and
algorithms (Chapters 5 and 6). Slides at
bspace

March
10: Anupam and
Nebojsa presented the chapter on Crypto and Game
Theory, here are their slides

March
17: Introduction to mechanism design
(Chapter 9)

March 31: Chris and Yaron
presented combinatorial auctions and approximation in mechanisms (Chapters
11-12)

April
7: Georgios
presented profit maximizing auctions (Chapter 13)

April
14: Bill and Jan will present
distributed algorithmic mechanism design (Chapter 14).

April
21: Anand, Ephrat, and Kory
presented cost sharing and cooperative games (Chapter 15)

April
28: Andrew presented online mechanisms
(Chapter 16), and Tom presented the price of anarchy and routing (Chapters 17
and 18)

May
5: Thomas presents price of anarchy in net design (Chapter 19), Jerry and Ronald
present prediction markets (Chapter 26)

May
12:

*There **will**
be a class May 12.*

*Extra office hours to
discuss the project: This Thu and Fri,
all day, email to make an appointment*

*Second Homework*

Part I, ** due April 14 If** you have not
selected a chapter and scheduled your presentation, do so, and notify the
instructor by due date. Also, if you
have made your presentation and have not turned in your 2-page summary, please
do so by the same deadline.

Part II, due April 21: ** Project outline.** Select a couple of interesting papers, read
them, and write a 1-page outline, emphasizing (a) main contributions, and (b)
open problems. One obvious avenue, but
not the only one, is to read papers related to/extending the topic of your
presentation. The project itself is a
~10-page paper on the same topic, due May 19.
If you need ideas, here are a few interesting recent papers:

Part III, due May 5:
Problems. Turn in your solutions
for any 4 of these:

1.
Suppose that you have players 1,…,n on a cycle of length n.
They all have the same strategy set S and the same utility function
mapping S^3 to the reals. Player 1 plays with players 2 and n, player 2
with 3 and 1, …, and finally player n with players 1
and n-1. That is, each player chooses a
strategy, and then the player i collects the payoff
dictated by the utility evaluated on the strategies of players i – 1, i, and i
+ 1. (a) Can you find efficiently if
this game has a pure Nash equilibrium?
(b) Repeat for a correlated equilibrium (here you must take care of the
problem that, strictly speaking, a correlated equilibrium is an exponential
object, and so you must first think how to represent it…). You may start by assuming that n is a
multiple of 3.

2.
Suppose that, in a 2-player game,
we pick any strategy of player 1, say strategy s, then the best response s’ to
it by player 2, and then the best response to s’’ by player 1. Show that, by combining these strategies, you
can create a pair of mixed strategies that are “near-best responses” to each
other. Generalize to three
players. Can you improve the two-player
result by continuing this way for more steps?

3.
Problems 13.1 and 13.2 from the
book.

4.
Problem 14.4

5.
Problem 11.4

*Important
rule about homeworks:*** **Collaboration
and consultation of sources is allowed and encouraged. It is, of course, acknowledged.