CS294 –P29:

Seminar on Algorithmic Game Theory

Instructor:  Christos H. Papadimitriou
Soda 389,  christos@cs, (510) 642-1559

Office Hours:  Monday and Thursday 5-6, and by appointment

Meets:  Tuesdays 10-1, Soda 310.

Course Format:  Lectures by the instructor and other participants.

Book:   Algorithmic Game Theory by Nisan, Roughgarden, Tardos, and V. Vazirani .  We’ll read much of the book, but also papers that go beyond its coverage.

Course Requirements:

 

Course Description

Ten years ago a new area was born in the interface between algorithms, game theory, and networking.  It has now grown to a mature field with hundreds of researchers and three conferences (ACM EC, WINE, and SAGT; look them up – watch out for the second one…), and an excellent edited book (see above).  In this class we’ll read most chapters of this book, and will probe the current frontiers of research in each by reading additional papers.  Participants will be expected to attend all meetings and participate in them, present one of the seminar’s topics, and to prepare a paper (ideally, containing at least some original work). Prerequisites:  Serious interest in the subject, and comfort with the subject matter and the level of technical exposition in the book. 

 

 

News and Handouts

 

Have you filled the course’s questionnaire?

 

First Homework, due February 3:

1.      Read this 1951 paper by Julia Robinson. Write a short exposition, explaining the proof and focusing on this question:  What is the convergence rate, ε as a function of t?   Improving this is an open problem.  Do you think it can be done?  Or could there be a lower bound?

2.     Read the abstracts of the chapters in the book, and select two or three as initial indications of the ones you would like to present.

Reading for the first three meetings:  Chapters 1 and 2 of the book.  Here is the full proof of the complexity result for Nash, here is a simplified exposition.

Meetings

 

Tue Jan 20:   Seminar inauguration, administrivia, Nash equilibria.

Tue Jan 27:   Review first lecture’s material.  Nash’s proof and complexity of Nash equilibria.

Feb 3:  Complexity and approximation of mixed Nash equilibria, correlated equilibria, extensive form games.

Feb. 10:  Extensive form games (selections from Chapter 3).  Also:  Costis Daskalakis on symmetry in games; here are his slides. 

Feb 17:  Learning in games (Chapter 4).   Presented by Isabelle, Jake, and Milos.

Feb 24:  General equilibrium theory, and algorithms (Chapters 5 and 6).  Slides at bspace

March 10:  Anupam and Nebojsa presented the chapter on Crypto and Game Theory, here are their slides

March 17:  Introduction to mechanism design (Chapter 9)

March  31:  Chris and Yaron presented combinatorial auctions and approximation in mechanisms (Chapters 11-12)

April 7:  Georgios presented profit maximizing auctions (Chapter 13)

April 14:  Bill and Jan will present distributed algorithmic mechanism design (Chapter 14).

April 21: Anand, Ephrat, and Kory presented cost sharing and cooperative games (Chapter 15)

April 28:  Andrew presented online mechanisms (Chapter 16), and Tom presented the price of anarchy and routing (Chapters 17 and 18)

May 5: Thomas presents price of anarchy in net design (Chapter 19), Jerry and Ronald present prediction markets (Chapter 26)

May 12:  

 

There will be a class May 12.

 

Extra office hours to discuss the project:  This Thu and Fri, all day, email to make an appointment

Second Homework

Part I, due April 14  If you have not selected a chapter and scheduled your presentation, do so, and notify the instructor by due date.  Also, if you have made your presentation and have not turned in your 2-page summary, please do so by the same deadline.

Part II, due April 21:  Project outline.  Select a couple of interesting papers, read them, and write a 1-page outline, emphasizing (a) main contributions, and (b) open problems.  One obvious avenue, but not the only one, is to read papers related to/extending the topic of your presentation.  The project itself is a ~10-page paper on the same topic, due May 19.  If you need ideas, here are a few interesting recent papers:

 

Part III, due May 5:  Problems.  Turn in your solutions for any 4 of these:

 

1.     Suppose that you have players 1,…,n on a cycle of length n.  They all have the same strategy set S and the same utility function mapping S^3 to the reals.  Player 1 plays with players 2 and n, player 2 with 3 and 1, …, and finally player n with players 1 and n-1.  That is, each player chooses a strategy, and then the player i collects the payoff dictated by the utility evaluated on the strategies of players i – 1, i, and i + 1.  (a) Can you find efficiently if this game has a pure Nash equilibrium?   (b) Repeat for a correlated equilibrium (here you must take care of the problem that, strictly speaking, a correlated equilibrium is an exponential object, and so you must first think how to represent it…).  You may start by assuming that n is a multiple of 3.

2.     Suppose that, in a 2-player game, we pick any strategy of player 1, say strategy s, then the best response s’ to it by player 2, and then the best response to s’’ by player 1.  Show that, by combining these strategies, you can create a pair of mixed strategies that are “near-best responses” to each other.   Generalize to three players.  Can you improve the two-player result by continuing this way for more steps?

3.     Problems 13.1 and 13.2 from the book.

4.     Problem 14.4

5.     Problem 11.4

  

Important rule about homeworks:  Collaboration and consultation of sources is allowed and encouraged.  It is, of course, acknowledged.