Algorithmic Game Theory
Computer Science 6840
Spring 2010
Office: 4130
Upson
4139 Upson Hall
phone:
255-0984
255 9296
email:
eva at cs.cornell.edu
e-mails: renatoppl or hufu [at] cs [dot] cornell [dot] edu
Office hour during the final weeks (starting
May 4th)
- Tuesday, May 4th Eva: 10-11am
- Thursday, May 6th
Hu Fu 5:15-6:15pm
- Friday, May 7th Renato 11am-12pm
- Saturday, May 8th and Sunday, May 9th, Renato,
call 607-280-5528 or email to make an appointment any time between
1-4pm.
- Monday May 10th
Renato 3:30- 5 pm
- Tuesday, May 11th Hu Fu
11am-12pm
- Wednesday May 12th Eva
1:30-2:30 pm
- Thursday, May 13th Hu Fu
11am-12pm
- Friday May 14th Eva
1:30-2:30 pm
- Sunday May 16th
Hu fu 10:30-11:30am
- Monday May 17th
Eva
10:30-11:30am
- Tuesday May 18th
Hu Fu 10:30-11:30am
- Wednesday May 19th Eva
10:30-11:30
starting on Wednesday, May 12th, Renato will hold office hours
on
Skype by appointment. Send him email to make an appointment.
You can also send us email to make an appointment..
Overview
Algorithmic Game Theory combines algorithmic thinking with game-theoretic,
or, more generally, economic concepts. The course will focus on problems
arising from, and motivated by, the Internet and other decentralized computer
networks. The most defining characteristic of the Internet is that it was not
designed by a single central entity, but emerged from the complex interaction of
many economic agents, such as network operators, service providers, designers,
users, etc., in varying degrees of collaboration and competition. The course
will focus on some of the many questions at the interface between algorithms
and game theory that arise from this point of view.
Book
We will use the book
- Algorithmic Game Theory.
(eds. Nisan, Roughgarden, Tardos, Vazirani)
and supplement it with additional papers. The book
is in reserve in the engineering library, and thanks to our progressive-minded
publisher you can read the entire book Algorithmic Game Theory (eds. Nisan,
Roughgarden, Tardos, Vazirani) online by clicking here (username=agt1user,
password=camb2agt)
Another excellent textbook that covers several of the course's topics is Shoham
and Leyton-Brown, Multiagent Systems,
Cambridge, 2008.
Problem sets
- Problem set
1 was Due Wednesday. Solutions are available on CMS
- Problem set
2 was Due Monday, March 8th. Solutions are available on CMS
- Problem set 3
was Due
Monday April 5th.
Solutions are available on CMS.
- Problem set 4 was Due Monday, April 26. Solutions
are available on CMS
- Final is be take home and require individual work. You have 7 days to
do the final, and can chose any day between Monday. May 3rd and Wednesday,
May 12th to start. The final will be available here
starting 4:35pm Wednesday on the 12th.
If the problem set deadline is causing problems, please let me know at least
a few days ahead of the deadline.
Topics week by
week, references, etc.
(Lecture topics, references and pointers to additional papers
are posted
here each week.)
- Monday, Jan 25: Introduction
(Chapter 1, pp 1-13)
- Wednesday, Jan 27 congestion
games, potential games, and existence of Nash. See Sections 17, 1,
8.2.1, 19.3.2.
- Monday, Feb 1, price of
anarchy and stability in potential games. See Section 19.3.3-4, and
18.4.2. The proof we only sketched in class is proof of Theorem 18.23 on
page 477.
- Wednesday, Feb 3, non-atomic
selfish routing, sections 18: existence of Nash, potential function, and
consequences.
- Monday, Feb 8: Price of Anarchy
for nonatomic congestion games: Section 18.4.1.
- Wednesday, Feb 10:
applications to springs, and capacity augmentation of Section 18.5.2
- Monday, Feb 15: proportional
resource allocation: sections 5.2-5.3 or see notes from earlier year:
part 1, and the first part of
part 2.
- Wednesday, Feb 17:
proportional sharing price of anarchy on a link, and characterization of
OPT and Nash on networks, see also the
part 3 of the notes.
- Monday, Feb 22: The local
connection game, section 19.2
- Wednesday Feb 24: Facility
location games are potential games Section 19.4
- Monday, March 1: Price of
Anarchy for facility location games
- Wednesday, March 3: randomized
Nash and Load balancing. See Section 1.3.4 and also Chapter 20
- Monday, March 8. Coarse
correlated equilibrium. See Section 1.3.6. and Chapter 4
- Wednesday, March 10. Weighted
majority algorithm. See notes.
- Monday, March 15: Prince of
anarchy bounds for correlated equilibria for utililiy. See the paper
Intrinsic
Robustness of the Price of Anarchy, by T. Roughgarden from STOC
'09.
- Wednesday, March 17: Prince of
anarchy bounds for correlated equilibria continued: congestion games.
- Monday, March 29. external
regret and internal regret, and algorithms for external regret, section 4.5
- Wednesday, March 31. Nash
equilibria, and no-regret algorithms in two person 0-sum games, section 4.4
- Monday, April 5 and Wednesday
April 7. Blackwell approachability and the learning algorithm regret
matching. See the paper
A Simple Adaptive
Procedure Leading to Correlated Equilibrium by Hart and Mas-Colell.
- Monday, April 12 and
Wednesday, April 14: are correlated equilibria computable? See
Computing
Correlated Equilibria in Multi-Player Games, by Papadimitriou and
Roughgarden,
- Monday April 19 through Monday
May 26, Nash equilibria and the Brauwer fixed point theorem, and Sperner
lemma, See Chapter 2.
- Wednesday April 28 and Monday
May 3rd: complexity classes FNP, and PPAD, and hardness of Nash. See Chapter
2.
- Wednesday May 5th. Networked
0-sum games. See Daskalakis and Papadimitriou,
On a
Network Generalization of the Minmax Theorem.
Course outline (subject to change):
- Introduction to Algorithms
and Games: (Chapter 1) games, Nash equilibria, solution concepts, and
examples
- Quantifying the Inefficiency
of Equilibria: (Part III: Chapters 17-21)
- Routing Games and
other congestion games: Nash equilibria
- Potential games:
Facility Location, Network Design
- Selfish Routing and Wardrop equilibria
- Other Network design
games
- Bandwidth sharing
Games
- Algorithmic Aspects of
Equilibria (Part I: Chapters 2-7)
- existence and
complexity of equilibria
- graphical games
- Learning in
games fictitious play, experts algorithm, no-regret algorithms;
convergence for zero-sum games
- correlated equilibria
and connection to learning in games
- Quantifying the
Inefficiency of learning outcomes
- Extensive form games
- Market equilibria
We may also consider a subset of the Part IV chapters depending on time
available and the interest of participants.
Pre-requisites
The course pre-requisites is background in
algorithms and graphs at the level of CS 4820. No prior knowledge of game
theory or economics will be assumed.
Course work
There will be 4 homework sets during the semester, and a final. You
may work in pairs on homeworks, and hand in a shared homework. You may discuss
homework questions with other students, but closely collaborate only with your
partner. The final is a non-cooperative version of the homework. Grades
and solutions to the homeworks will be kept in CMS.
Classes on similar topics at other
universities:
ˇ
Earlier version of this
course
ˇ
Algorithmic
Aspects of Game Theory by Christos Papadimitriou
ˇ
Topics in Algorithmic Game
Theory by Tim Roughgarden and Jason Hartline
ˇ
Algorithmic
Mechanism Design by Jason Hartline
ˇ
Topics in Algorithmic Game
Theory by Costis Daskalakis