Email: kirk@cs.pitt.edu
chung@cs.pitt.edu
Phone : 412-624-8844
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 |
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Wednesday Jan 9 |
Lemke-Howson algorithm for general 2-person 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 Lemke-Howson algorithm to this Nash Equilibrium until you get to a new Nash Equilibrium. Your first step will be arbitrary. Show the path on the 3-D and 2-D spaces shown in the notes. |
Monday Jan 14 |
Complexity of Nash Equilbrim: Reduction to linear programming for zero-sum 2-person games Sperner's lemma -> Brower Fixed point -> Existence of Nash |
Chapter 2 Good notes from a class taught by Christos Papadimitriou |
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Wednesday Jan 16 |
NP-hardness of deciding if > 1 mixed Nash Equilibrium in a 2-person 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.
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Monday Jan 21 No class MLK day |
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Wednesday Jan 23 Class cancelled |
L |
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Monday Jan 28 Guest Lecture Katrina Ligett |
Learning, Regret Minimization, and Equilibria |
Chapter 4 |
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Wednesday Jan 30 |
KKT-conditions Resource Allocation Markets
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Section 5.13 Slides and Slides by Vijay Vazirani |
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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?
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Wednesday Feb 6
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Social Choice: Arrow's Impossibility Lemma and Gibbard-Satterthwaite |
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:
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Monday Feb 11 Christine will be speaking |
Intro to Inefficiency of Equilibria |
Sections 17.1-17.2.3 |
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Wednesday Feb 13 Christine will be speaking |
Routing Games |
Sections 18.1-18.4 |
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Monday Feb 18 Christine will be speaking |
Network Formation Games: a local connection game |
Sections 19-1-19.2 |
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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 9.3-9.4 |
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 10.3-10.4 |
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Monday March 3 |
Combinatorial Auctions: The greedy algorithm for single minded bidders |
Section 11.2 |
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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 |
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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 |
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Monday March 24 |
Cost Sharing |
Chapter 15 |
Group Homework: Problem 15.2 |
Wednesday March 26 |
Cascading Behaviour in Networks |
Chapter 24 |
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Monday March 31
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Lory's Presentation on Sponsored Search |
Chapter 28 |
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Wednesday April 2 |
Shenoda's Presentation on Selfish Load Balancing |
Chapter 20 |
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Monday April 7 No Class |
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Wednesday April 9 No Class |
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Monday April 14 |
Josh's Presentation on Reputation Systems |
Chapter 27 |
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Wednesday April 16 |
Rich's Presentation on Biological Applications of Games |
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Monday April 21 |
Tomas' Presentation on Bayesian Approaches |
Paper by Jim Ratliff |
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Wednesday April 23 |
Panickos' Presentation on Peer to Peer Applications of Games |
Chapter 23 |
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