Email: kirk@cs.pitt.edu
chung@cs.pitt.edu
Phone : 4126248844
Course Format
The instructors will present the initial lectures. Each student will be expected to lead some lectures/discussions later in the semester covering some portion of the text. One or two exercises may be assigned from each chapter to provide some practice using the concepts from the chapter.
Class Time and Location
Mondays and Wednesdays (and maybe a rare Friday to make up for classes missed due to instructors' travels to academic conferences) from 1:00 to 2:15 in room 5313 of the Sennott Square building.
Tentative Schedule
Date 
Topic 
Reference 
Homework due at the start of next class. Occasionally I will ask someone to present the homework 
Monday Jan 7 
Definition: Strategic game, dominance, Pareto efficiency/optimality, pure Nash equilibrium, mixed Nash equilibrium 
Chapter 1 

Wednesday Jan 9 
LemkeHowson algorithm for general 2person games 
Chapter 3 is tough sledding Insteead try good slides from class taught by Michael Lewiki 
Homework: Consider the game in Lewiki's notes. Find a mixed Nash equilibrium for the game. Apply the LemkeHowson algorithm to this Nash Equilibrium until you get to a new Nash Equilibrium. Your first step will be arbitrary. Show the path on the 3D and 2D spaces shown in the notes. 
Monday Jan 14 
Complexity of Nash Equilbrim: Reduction to linear programming for zerosum 2person games Sperner's lemma > Brower Fixed point > Existence of Nash 
Chapter 2 Good notes from a class taught by Christos Papadimitriou 

Wednesday Jan 16 
NPhardness of deciding if > 1 mixed Nash Equilibrium in a 2person game 
Paper by Conitzer and Sandholm Slides for the paper Slides revised by the students 
Group Homework: Elaborate/Improve on the first page of these Slides to make the proof more complete/convincing/illuminating. In particular explain why:
You may also change the instance constructed game (say by adding infinity payoffs) if you think that that helps. Email me the slides, and I will post your revision. Don't get carried away, I am thinking that this should take 1 or at most 2 hours.

Monday Jan 21 No class MLK day 



Wednesday Jan 23 Class cancelled 
L 


Monday Jan 28 Guest Lecture Katrina Ligett 
Learning, Regret Minimization, and Equilibria 
Chapter 4 

Wednesday Jan 30 
KKTconditions Resource Allocation Markets

Section 5.13 Slides and Slides by Vijay Vazirani 

Monday Feb 4 
Fischer's Linear Market 
Section 5.2  5.11 Slides by Amin Saberi 
Group homework: Consider a market of goods and buyers where the utility only increases as the square root of the quantity of good received. That is, a buyer i gets utility u_{i,j} (x_{i,j})^{1/2} from x_{i,j} units of good j. It is probably more realistic to assume that utility is a concave function of quantity.
What, if anything, goes wrong if one tries to apply the algorithm in section 5.8 for Fischer's linear case to this market? Don't worry about running time, concentrate on correctness of the algorithm. If what goes wrong is minor, can it be easily fixed?

Wednesday Feb 6

Social Choice: Arrow's Impossibility Lemma and GibbardSatterthwaite 
Section 9.2 Notes from class by Christos Papadimitriou 
Group Homework: In the proof of Arrow's Impossibility Lemma that I did in class (basically the same proof as in the book) we consider the sequence F(pi_0) ... F(pi_n). Recall that F satisfied the conditions of unanimity and independence of irrelevant alternatives. It is easy to see that there must exist a k such that b > a if F(pi_j) for j < k and a > b in F(pi_k). That is the preference flips at k. In my argument I assumed that it was then also the case that a > b in F(pi_j) for j > k. That is, once the preference flips, it has to stay flipped. Shenoda pointed out that it at least wasted obvious that this is true, that is, it is possible that the preference between a and b could flip several times. Your goal is to determine which of the following is true:

Monday Feb 11 Christine will be speaking 
Intro to Inefficiency of Equilibria 
Sections 17.117.2.3 

Wednesday Feb 13 Christine will be speaking 
Routing Games 
Sections 18.118.4 

Monday Feb 18 Christine will be speaking 
Network Formation Games: a local connection game 
Sections 19119.2 

Wednesday Feb 20 Christine will be speaking 
Network Formation Games: A global connection game and the Potential Function Method 
Section 19.3 
Group Homework: Problem 19.14 
Monday Feb 25 
Mechanisms with Money: VCG, Clark Pivot Rule 
Sections 9.39.4 
Group Homework: Consider the auction problem of selling k identical items to k different bidders. Is have the i^th highest bidder pay the bid of the (i+1)st highest bid truthful? 
Wednesday Feb 27 
House Allocation and Stable Marriage 
Sections 10.310.4 

Monday March 3 
Combinatorial Auctions: The greedy algorithm for single minded bidders 
Section 11.2 

Wednesday March 5 
Combinatorial Auctions: Walrasian Equilibrium and the LP relaxation Communication Complexity 
Section 11.3 Section 11.6 
Group Homework: Prove Lemma 11.13 using the KKT conditions (or LP duality) Group Homework: Problem 11.9 from the text 
Spring Break 



Monday March 17 
BGP Routing 
Section 14.3 
Group Homework: Can you come up with a precise formulation of Theorem 14.7 that is both interesting and (at least plausibly) true. The main issue in the proof that follows is "What is the domain of quantification when it is claimed that each AS gets their most valued route?" 
Wednesday March 19 
Cost Sharing 
Chapter 15 

Monday March 24 
Cost Sharing 
Chapter 15 
Group Homework: Problem 15.2 
Wednesday March 26 
Cascading Behaviour in Networks 
Chapter 24 

Monday March 31

Lory's Presentation on Sponsored Search 
Chapter 28 

Wednesday April 2 
Shenoda's Presentation on Selfish Load Balancing 
Chapter 20 

Monday April 7 No Class 



Wednesday April 9 No Class 



Monday April 14 
Josh's Presentation on Reputation Systems 
Chapter 27 

Wednesday April 16 
Rich's Presentation on Biological Applications of Games 


Monday April 21 
Tomas' Presentation on Bayesian Approaches 
Paper by Jim Ratliff 

Wednesday April 23 
Panickos' Presentation on Peer to Peer Applications of Games 
Chapter 23 
