**Instructor: ** Christos
H. Papadimitriou

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

**Office Hours: **Wednesdays
2-3, and by appointment

**Meets:** Tuesdays 3:30-5:30pm,
in Soda 306

**Course Format: **Lectures
by the instructor, occasionally by guests.

**Course Requirements:**

- 2-3 problem sets
- students will be expected to select a topic (among those pertinent to the scope of the course but not covered in the course) read the literature on it, and write an appraisal that is as original as feasible. Collaboration is possible if appropriate.
- students will also be expected to scribe lecture notes, in collaboration with the instructor.
- this is a 2-unit course

There have been many instances in the recent literature in which algorithmic thinking is combined with game-theoretic, or, more generally, economic concepts to address problems arising in the context of the Internet. The purpose of this course is to seize this moment and promote this interaction. The emphasis will be on mathematically sophisticated techniques in the interface between algorithms and game theory, as well as their applications to the Internet. Topics will include some of the following (the list will crystallize gradually,with references and/or links to documents):

- Nash equilibrium and general equilibrium
- Refinements of equilibrium concepts
- Social choice theory
- Mechanism design
- Multicast pricing
- Worst-case equilibria and "the price of anarchy"
- Combinatorial auctions
- Games played by automata and bounded rationality
- Evolutionary game theory and repeated games
- Fairness in cooperative games
- Economic aspects of:
- the structure of the Internet graph
- privacy
- clustering

**Lectures and Notes**

Friday January 19: Introduction A talk at SODA 2001 (powerpoint presentation)

Tuesday January 23: Existence of equilibria

Tuesday January 30: Variants of the concepts of "game" and "rational play"

Tuesday February 6: Social choice theory

Tuesday February 13: Mechanism design

Tuesday February 20: Algorithmic mechanism design (see papers by Nisan; also, notes)

Tuesday February 27: Scott Shenker will lecture
on Learning
and Implementation on the Internet

(see also two
related papers and his
slides
from
the lecture)

Tuesday March 6: Cost sharing in multicasts (see
paper by Feigenbaum
*et
al*. and other papers below)

Tuesday March 13: Combinatorial auctions (papers below, and notes)

Tuesday March 20: First half: Combinatorial auctions (continued) Second half: Talk by Anna Karlin on spectral methods in information retrieval (first paper in her web page).

Tuesday March 27: Spring Break

Tuesday April 3: (No lecture on Thursday either....)

Tuesday April 10: Coalitional games and solution concepts

Tuesday April 17: Coalitional games and solution concepts (cont.)

Tuesday April 24: Multi-objective optimization

Tuesday May 1: Powerlaws in the
Internet, the Web, and the Economy

(see lecture
notes, the papers below, and this
course at UMass )

Tuesday May 8: Continued, probably

**Problem Sets**

First problem set, due February
20 **IMPORTANT ADDITION:
Please include in your problem set solutions a paragraph with your thoughts
about the project.**

**Readings**

Two books I recommend:

Osborne and Rubinstein, *A
Course in Game Theory*

David Kreps, *A Course in Microeconomic Theory*

The following papers will either be covered in the lectures,
or are suggested readings for the project part of the course.

Papers on algorithmic mechanism design:

Algorithms for Selfish Agents
by Nisan

Algorithmic Mechanism Design
by Nisan and Ronen

A solution to Vickrey
shortest paths by Suri and Hershberger

Papers on internet congestion and game theory/economics:

Resource Pricing and the Evolution
of Congestion Control by Gibbens and Kelly

A Modest Proposal for Preventing
Internet Congestion by Odlyzko

Optimization Problems in Congestion
Control by Karp, Koutsoupias, Papadimitriou, Shenker

Differential QoS and Pricing
in Networks by Key and McAuley

Pricing Congestible Resources, Chapter
4 by Varian

Stackelberg Scheduling by Roughgarden

Papers on the price of anarchy:

Worst-case
Equilibria by Koutsoupias and Papadimitriou

How Bad is Selfish Routing?
by Roughgarden and Tardos

Papers on combinatorial auctions:

A survey

Bidding and Allocation in Combinatorial
Auctions by Nisan

Iterative Combinatorial Auctions:
Theory and Practice by Parkes and Ungar

Optimal Auction Design by
Parkes

Graph-theoretic auctions by Akcoglu,
Aspnes, *et al*.

Papers on multicast auctions:

Incentive-compatible On-line Auctions
by Lavi and Nisan

"Cost Sharing of a Homogeneous Good: Average versus Serial Methods,"
by
Moulin and Shenker

Sharing
the Cost of Multicast Transmissions by Feigenbaum, Papadimitriou, Shenker

Strategyproofness via LP Duality
by Vijay Vazirani and Jain

Auctions of Digital Goods by Goldberg,
Hartline, and Wright

Papers on repeated games:

Bounded Rationality and Computational
Complexity by Papadimitriou and Yannakakis

Rational Learning and Nash Equilibrium
by Kalai and Lehrer

Papers on multi-objective optimization:

The Approximability
of Trade-offs by Papadimitriou and Yannakakis

An application of social choice to document ranking

Rank Aggregation, Spam Resistance, and Social
Choice by Dwork Kumar Moni Naor and Sivakumar

Papers on power laws:

Stochastic models of the web graph
by Kumar et al.

Powerlaws in the internet topology
by Faloutsos^{3}

Highly optimized tolerance by Carlson
and Doyle ( plus another paper by them )

Sally Floyd's web
page on self-similarity in the Internet

Papers on game theory:

My STOC 2001 paper (most topics in the
class reviewed).

Strategic Information Transmission
by Crawford and Sobel

A survey paper: Games, Computers,
and OR by Kalai

A dynamics that, in some sense and cases, converges to the Nash equilibrium:

Nash
Convergence of Gradient Dynamics in General-Sum Games, by Singh Kearns
and Mansour

A representation of games, with an algorithm for computing Nash equibria
in some

special cases Graphical models in
game theory Kearns Littman and Singh