COS 597F

Open Problems in Algorithmic Game Theory

Princeton University

 

Instructor: Matt Weinberg (smweinberg (at) princeton (dot) edu).

 

Piazza: https://piazza.com/class/jlxxavpqz85n2

 

Announcements will be posted below:

-         Homework 1 is now out below.

 

Homework: Homeworks will be posted below when they become available. Here is a LaTeX template you may use for the homework, and here is a short guide to LaTeX.

 

-         Homework 1. Due 11/9. Submit to Tigerfiles here.

-         Homework 2. Due 12/10. Submit to Tigerfiles here.

 

References: You may find the following references helpful.

AA: The fall 2017 iteration of Advanced Algorithms.

EC: The spring 2018 iteration of Economics and Computation.

The AGT Book: The AGT book, especially Chapters 11/12 on combinatorial auctions. (Click link --> resources --> Algorithmic Game Theory --> Algorithmic Game Theory).

MDnA: Mechanism Design and Approximation (relevant to second half of class on Bayesian mechanism design.).

 

Lecture Notes: I will post the lecture notes I use to present on Piazza. These lecture notes are written hastily and likely contain errors, but may be helpful as a reminder for what was covered in class, or for the cited references.

 

Date

Topic

Reading Material

9/12

Combinatorial Auctions: Introduction, Definitions, Approximation with Value Queries.

See Piazza.

9/17

Combinatorial Auctions: More Approximation with Value Queries.

See Piazza.

9/19

Combinatorial Auctions: Walrasian Equilibria and Gross Substitutes.

See Piazza.

9/24

Combinatorial Auctions: Configuration LP.

See Piazza.

9/26

Combinatorial Auctions: Lavi-Swamy Reduction.

See Piazza.

10/1

Combinatorial Auctions: Simultaneous Protocols.

See Piazza.

10/3

Combinatorial Auctions: Lower bounds.

See Piazza.

10/8

Combinatorial Auctions: Truthful mechanisms I

See Piazza.

10/10

Combinatorial Auctions: Truthful mechanisms II

See Piazza.

10/15

Combinatorial Auctions: Bayesian setting I.

See Piazza.

10/17

Combinatorial Auctions: Bayesian setting II.

See Piazza.

10/22

Combinatorial Auctions: Taxation Complexity.

See Piazza.

10/24

Combinatorial Auctions: VC-Dimension Lower Bounds.

See Piazza.

10/29

Fall Break

 

10/31

Fall Break

11/5

Myerson’s Optimal Auction.

See Piazza.

11/7

Revisiting Myerson via duality.

See Piazza.

11/12

Multi-Item Auctions: Examples.

See Piazza.

11/14

Multi-Item Auctions: Basic Revenue Bounds.

See Piazza.

11/19

Multi-Item Auctions: One Additive Buyer.

See Piazza.

11/21

Thanksgiving

11/26

Multi-Item Auctions: One Subadditive Buyer.

See Piazza.

11/28

Multi-Item Auctions: Correlated Values.

See Piazza.

12/3

Multi-Item Auctions via Duality.

See Piazza.

12/5

Multi-Item Auctions: Many Subadditive Buyers.

See Piazza.

12/10

Multi-Item Auctions: Deterministic mechanisms.

See Piazza.

12/12

Price of Anarchy for Auctions.

See Piazza.