Spring 2014

Office: 316 Gates Hall 336 and 324 Gates Hall

phone: 255-0984

email: eva at cs.cornell.edu e-mails: jalaly@cs.cornell.edu and rad@cs.cornell.edu

- Wednesday,
Jan 23 introduction and Brasss paradox and the
tragedy of the commons.

Notes for lecture from a previous year.

- Friday,
Jan 25 on discrete congestion games and the existence of equilibria.

Notes for lecture from a previous year.

- Monday,
Jan 27: more on potential function for congestion games, and complexity of
finding equilibria

Additional
reference: Alex Fabrikant, Christos
Papadimitriou, and Kunal Talwar
On the
complexity of pure Nash equilibria

- Wednesday,
Jan 29 and Friday, Jan 31; existence of Nash equilibria and PPAD

Notes
from a previous year

Please
try the online
Rock-Paper-Scissor game.

- Monday,
Feb 3: multiplicative weight algorithm for binary prediction.

See sections 3-4 of the notes
from 2007.

- Wednesday,
Feb 5, Hedge algorithm for prediction

See
sections 5 of notes
and some of sections 4 of notes
from 2007.

- Friday,
Feb 7: learning and regret in
games.

See
section 2 of the notes
from 2007, and the first page of the notes
from 2012.

- Monday,
Feb 10, Coarse correlated equilibria of finite games, and learning
outcomes

See notes
from 2012

- Wednesday,
Feb 12: non-atomic congestion games and the price of anarchy

See notes
from 2012.

- Friday,
Feb 14: non-atomic congestion games and the price of anarchy (cont.)

See notes
from 2012

- Monday,
Feb 17 break
- Wednesday,
Feb 19, atomic congestion games and the price of anarchy
- Friday,
Feb 21, smooth games minimizing cost and the price of anarchy

See notes
from 2012

- Monday,
Feb 24, Utility maximization games (Guest lecture by Vasilis Syrgkanis)

Notes from Vasilis. See also the paper * Intrinsic
Robustness of the Price of Anarchy *by Tim Roughgarden

- Wednesday,
Feb 26: Valid utility games are (1,1) smooth

See notes
from 2012

- Friday,
Feb 28: the facility location game

See notes
from 2012

- Monday,
March 3: outcomes of best responses for the facility location game

See notes
from 2012

- Wednesday,
March 5, Price of stability of cost sharing game.

See notes
from 2012

- Friday,
March 7, second price auction, Guest lecture by Rad Niazadeh

Similar notes
from 2012

- Monday,
March 10, Bayesian Nash equilibrium and First price auction

Notes
from 2012

- Wednesday,
March 12, the VCG mechanism

Notes from
2012

- Friday,
March 14, Smooth auctions and the price of anarchy in auction games

- Monday,
March 17, examples of smooth auctions: first price

- Wednesday,
March 19, more examples of smooth auctions: all pay, and first price unit
demand bidders

·
Friday, March 21,
smooth games and the Bayesian Price of Anarchy

·
Monday, March 24,
Generalized second price action (GSP)

·
Wednesday, March 26, price of anarchy for GSP

Notes by Jonathan
DiLorenzo improved in April 14.

·
Friday, March 28, price of anarchy for
mechanisms based on greedy algorithms

·
Monday, April 7,
smoothness, and second price item auction with unit demand bidders

·
Wednesday, April 9,
second price item auction with fractionally submodular
valuations

·
Friday, April 11,
classes of valuations: submodular, subadditive and fractionally subadditive

See notes

·
Monday, April 14, on
Bandwidth sharing in a single link, and price equilibrium of the fair sharing game.

See
notes from 2012.

·
Wednesday, April 16,
price of anarchy analysis for fair sharing on a single link.

See notes
from 2012.

·
Friday, April 18, on
Bandwidth sharing in a network.

See notes
from 2012.

·
Monday, April 21, more
on Bandwidth sharing in a network.

See notes,
from 2012, and also the paper R. Johari and J.N. Tsitsiklis
(2004). Efficiency
loss in a network resource allocation game.

·
Wednesday, April 23, Walrasian pricing equilibrium.

·
Friday, April 25, Walrasian pricing equilibrium, and existence of optimal
Nash in the GSP game.

·
Monday, April 28, Vasilis
Syrgkanis on sequential auction games

See the paper Sequential Auctions and Externalities

·
Wednesday, April 30,
Arrow-Debreu market equilibrium

·
Friday, May 2,
Arrow-Debreu market equilibrium cont, and Fischer
markets

See notes
from 2012. See also the course on Computation of
equilibria by Amin Saberi

·
Monday, May 5, revenue
equivalence

See notes
from 2012

·
Wednesday, May 7^{th},
Revenue versus an extra bidder: Bulow Klemperer

See notes
from 2012, and the paper by Bulow Klemperer Auctions
versus negotiations.

See also the
courses

Problem set 1
was due Friday, February 14, it is now graded and solutions and comments are
available on CMS.

Problem set 2
was due Wednesday, March 5, it is now graded and solutions and comments are
available on CMS.

Problem set 3 was due Tuesday, March 24, 2014, it is now graded and solutions and comments are available on CMS.

Proposal for the final project was
due, Friday March 28.

Problem set 4
was due Monday, April 21^{st}, it is
now graded and solutions and comments are available on CMS.

Final
project is due Wednesday, May 7^{th}. See more details at Course work
below.

Take
home final is available starting May 12^{th}. Final is cumulative, and is a
non-cooperative version of the homeworks. You can choose
any 72 hour period to do the final during May 12-20, **but need to be finished by 5pm on Tuesday the 20th.** Office hours
during the final week are posted on Piazza.

· Sample tex file from Chris Liu’s notes

· Video of all previous run of this class are available at www.videonote.com/Cornell

*Algorithmic Game Theory*. eds. Nisan, Roughgarden, Tardos, Vazirani (username=agt1user, password=camb2agt), Cambridge, 2007.- M. Osborne, A. Rubinstein, A course in Game Theory, MIT Press, 1994.
*Approximation in Economic Design*by Jason Hartline- Multiagent Systems, by Shoham and Leyton-Brown, Cambridge, 2008.
- Prediction, Learning, and Games , by Cesa-Bianchi and Lugosi
- The Theory of Learning in Games , by Fudenberg and Levine
- For a nice introduction to Game Theory look at Ken Binmore: Game Theory: a Very Short Introduction, Oxford University Press.

Rough course outline (subject to change):

- Introduction
to Algorithms and Games:
- Games and examples
- Solution concepts: Nash equilibria, Bayesian Nash, learning
in games and correlated Nash
- Quantifying
the Inefficiency of Equilibria:
- Best and worst Nash,
- Quality of learning outcome.
- Strong price of anarchy.

·
Games we will discuss
include

- 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
- Auction Games: Simultaneous, Sequential and Greedy Auctions, Generalized Second Prize
- Market games: market clearing prices, and related games.
- Matching games
- Mechanism Design
- Basics: second-price auction, Vickrey-Clarke-Groves mechanism;
- Bayesian Mechanism Design;
- Revenue equivalence
- Bayesian Approximation
- prior-independent mechanisms;

Course work consists of **4 homework sets, a final, a final project, and
possibly scribe notes.** You may discuss homework questions with other
students, but need to write down the solutions on your own.** The final is a
non-cooperative version of the homework. **Extra credit will be available for
solving more homework problems than required or by improving wikipedia pages about topics discussed in class. Grades and
solutions to the homeworks will be kept in CMS.

The project should be a research-like experience (understand what is known about about a research problem, and try to advance knowledge). You can base projects on recent research papers: understanding what they are doing, and attempting to improve the model or result. Or you can base projects on your own research interests. You need to write your project result in format of a paper, expected to be 6-10 pages long (definitely no longer than 10).

Course grade is determined roughly as

- Homeworks: 10% each
- project proposal 5%
- project 25%
- take home final 30%

Extra credit can be earned by solving all problem on the problem set, or by improving pages on wikipedia related to the course. Extra credit is very useful for getting an A+, and can also be used can to partially make up missing credit on homeworks, and the final.

Algorithmic Game Theory combines algorithmic thinking with game-theoretic, or, more generally, economic concepts. The course will study a range of topics at this interface. The only prerequisite to the course is mathematical maturity. An A- or better in CS 4820 is great, or a course at a similar level in a different department.

**Classes on similar topics at other
universities: **

· Earlier version of this course

· Price of Anarchy by Jason Hartline

· Algorithmic Mechanism Design by Jason Hatrline

· Algorithmic Game Theory by Tim Roughgarden

· Games, Decision, and Computation by Costis Daskalakis and Silvio Micali