**Instructor:** Tim
Roughgarden (Office hours: Mondays and Wednesdays after class.)

**Teaching Assistants:**

- Kostas Kollias (Office hours: Thursdays 9 AM-Noon, in Gates B24A. Email: kkollias "at" stanford.edu)
- Okke Schrijvers (Office hours: Tuesdays 1-4 PM, in Gates 463A. Email: okkes "at" stanford.edu)

**Time/location:**
2:15-3:30 PM on Mondays and Wednesdays in Littlefield 103.

**Piazza site:** here

**Course description:**
Broad survey of topics at the interface of theoretical computer science
and economics. Introduction to auction and mechanism design,
with an emphasis on computational efficiency and robustness.
Introduction to the "price of anarchy", with applications to networks.
Algorithms and complexity theory for learning and computing Nash and
market equilibria.
Case studies
in Web search auctions, wireless spectrum auctions, matching markets,
network routing, and security applications.

**Prerequisites**: basic algorithms and complexity (154N and 161, or equivalent). No prior knowledge of economics or game theory is required.

**Course requirements:**
All students are required to complete weekly exercise sets, which fill
in details from lecture.
Students taking the course for a letter grade are also required to
complete biweekly problem sets, which supplement the material covered
in lecture.
Students are encouraged to form groups (up to three students) to
complete the problem sets.
There will also be occasional extra credit problems and opportunities.
**No late assignments accepted.**

- A LaTeX template that you can use to type up solutions. Here and here are good introductions to LaTeX.

**All lecture notes and exercise sets in one PDF.**

**Lecture videos and notes (beta versions)**

- Lecture 1 (Introduction): Video Notes
- Lecture 2 (Mechanism Design Basics): Video Notes
- Lecture 3 (Myerson's Lemma): Video Notes
- Lecture 4 (Algorithmic Mechanism Design): Video Notes
- Lecture 5 (Revenue-Maximizing Auctions): Video Notes
- Lecture 6 (Simple Near-Optimal Auctions): Video Notes
- Lecture 7 (VCG Mechanism): Video Notes
- Lecture 8 (Spectrum Auctions): Video Notes
- Lecture 9 (Beyond Quasi-Linearity): Video Notes
- Lecture 10 (Kidney Exchange, Stable Matching): Video Notes
- Lecture 11 (Selfish Routing and the POA): Video Notes
- Lecture 12 (Network Over-Provisioning): Video Notes
- Lecture 13 (Hierarchy of Equilibrium Concepts): Video Notes
- Lecture 14 (Smooth Games): Video Notes
- Lecture 15 (Best-Case and Strong Nash Equilibria): Video Notes
- Lecture 16 (Best-Response Dynamics): Video Notes
- Lecture 17 (No-Regret Dynamics): Video Notes
- Lecture 18 (Swap Regret; Minimax): Video Notes
- Lecture 19 (Pure NE and PLS-Completeness): Video Notes
- Lecture 20 (Mixed NE and PPAD-Completeness): Video Notes
- The CS364A Top 10 List

**Exercise and problem sets:**

- Exercise Set #1 (Out Wed 9/25, due by class Wed 10/2.)
- Exercise Set #2 (Out Wed 10/2, due by class Wed 10/9.)
- Exercise Set #3 (Out Wed 10/9, due by class Wed 10/16.)
- Exercise Set #4 (Out Wed 10/16, due by class Wed 10/23.)
- Exercise Set #5 (Out Wed 10/23, due by class Wed 10/30.)
- Exercise Set #6 (Out Wed 10/30, due by class Wed 11/6.)
- Exercise Set #7 (Out Wed 11/6, due by class Wed 11/13.)
- Exercise Set #8 (Out Wed 11/13, due by class Wed 11/20.)
- Exercise Set #9 (Out Fri 11/22, due by noon Fri 12/6.)

- Problem Set #1 (Out Wed 9/25, due by noon Fri 10/11.)
- Problem Set #2 (Out Wed 10/9, due by noon Fri 10/25.)
- Problem Set #3 (Out Wed 10/23, due by noon Fri 11/8.)
- Problem Set #4 (Out Wed 11/6, due by noon Fri 11/22.)
- Take-Home Final (Out Wed 11/20, due by noon Fri 12/13.)

**Primary references:**

- Nisan/Roughgarden/Tardos/Vazirani (eds),
*Algorithmic Game Theory*, Cambridge University, 2007.- Also available free on the Web, see here.

- To get a sense for the course in a nutshell:
- T. Roughgarden, Algorithmic Game Theory (CACM July 2010);
- T. Roughgarden, An Algorithmic Game Theory Primer (an earlier and longer version).

- For the first four weeks, most of what we cover is also covered in Hartline's book draft. (Feedback is solicited here.)
- Another excellent textbook that covers several of the
course's topics is Shoham and Leyton-Brown,
*Multiagent Systems*, Cambridge, 2008.

**Lecture 1 (Mon 9/23):**Introduction. The 2012 Olympic badminton scandal. Selfish routing and Braess's Paradox. Can strategic players learn a Nash equilibrium?

Readings:- J. Hartline and R. Kleinberg, Badminton and the Science of Rule Making, Huffington Post, 2012.
- Video of the first controversial badminton match.
- Braess's Paradox: Chapter 1 of T. Roughgarden,
*Selfish Routing and the Price of Anarchy*(MIT Press, 2005), available here via the "Sample Chapter" link. - Physical demonstrations of Braess's Paradox, by alumni of CS364A: #1 #2 #3
- Basic games and equilibrium notions: AGT book, Sections 1.1.1--1.3.4.

**Lecture 2 (Wed 9/25):**Mechanism design basics. How would you bid in a first-price auction? The Vickrey auction and dominant-strategy implementations. Case study: sponsored search auctions.

Readings:- The Vickrey auction: AGT book, Section 9.3.1, 9.3.2, and 9.3.5; and/or Section 1 or these old CS364B notes.
- Pages 1-8 of Hartline's book.
- Optional sponsored search readings: AGT book, Sections 28.1-28.3.1. See also this CS364B course for tons of subtopics and references on sponsored search auctions (circa late 2007).

**Lecture 3 (Mon 9/30):**Characterization of single-parameter DSIC mechanisms (Myerson's Lemma). Readings:- AGT book, Sections 9.4.1--9.4.2 and 9.5.4--9.5.6. Optionally, see also Section 4 in this FOCS '01 paper by Archer and Tardos.
- Sections 2.6 and 3.1 of Hartline's book.

**Lecture 4 (Wed 10/2):**DSIC sponsored search auctions. Knapsack auctions and algorithmic mechanism design. Revelation Principle. Readings:- See Lecture 2 for sponsored search readings.
- AGT book, Sections 9.4.3 (Revelation Principle) and 12.1 (introduction to algorithmic mechanism design).
- Sections 2.10 and 3.2 of Hartline's book.
- Knapsack review videos: Dynamic programming solutions part 1 part 2 part 3; greedy 0.5-approximation algorithm and analysis part 1 part 2 part 3; (1-epsilon)-approximation algorithm part 1 part 2
- Optional: How To Think About Algorithmic Mechanism Design, a 90-minute tutorial by your instructor at FOCS '10. Video
- The latest results on black-box reductions for single-parameter problems are due to Chawla/Immorlica/Lucier, STOC '12.

**Lecture 5 (Mon 10/7):**The challenge of revenue maximization. Bayesian optimal auctions. Readings:- AGT book, Sections 13.1-13.2.
- Sections 3.3.1-3.3.3 of Hartline's book.

**Lecture 6 (Wed 10/9):**The Prophet Inequality. Simple near-optimal auctions. Prior-independent auctions and the Bulow-Klemperer theorem. Readings:- Sections 4.2, 5.1, 5.2.1 of Hartline's book.

**Lecture 7 (Mon 10/14):**Case study: reserve prices in Yahoo! keyword auctions. Multi-parameter mechanism design and the VCG mechanism. Introduction to combinatorial auctions. Readings:- Ostrovsky/Schwarz, Reserve Prices in Internet Advertising Auctions: A Field Experiment, 2009.
- AGT book, Sections 9.3.3-9.3.4 and 11.1.
- See also these old CS364B notes on combinatorial auctions and the VCG mechanism.
- Cramton/Schwartz, Collusive Bidding in the FCC Spectrum Auctions, 1999.

**Lecture 8 (Wed 10/16):**Case study: wireless spectrum auctions. Readings:- Cramton/Shoham/Steinberg (eds.), Combinatorial Auctions,
MIT Press, 2006.
- Chapter 4 (Cramton) covers simultaneous ascending auctions.
- Chapter 5 (Ausubel/Cramton/Milgrom) discusses how to add a final "proxy" round with package bidding.

- Milgrom, Chapter 1 of
*Putting Auction Theory to Work*, Cambridge, 2004. - Goeree/Holt, Hierarchical Package Bidding, about bidding only on predefined packages.
- Milgrom/Segal, Deferred-Acceptance Heuristic Auctions, 2013. Describes the proposed format for the reverse auction in the upcoming FCC double auction.

- Cramton/Shoham/Steinberg (eds.), Combinatorial Auctions,
MIT Press, 2006.
**Lecture 9 (Mon 10/21):**Beyond quasi-linearity. The clinching auction for bidders with budgets. The top trading cycle algorithm for housing allocation.- Dobzinski/Lavi/Nisan, Multi-unit Auctions with Budget Limits, FOCS '08.
- AGT book, Section 10.3.

**Lecture 10 (Wed 10/23):**Case study: kidney exchange. Stable matching.- Roth/Sönmez/Ünver, Kidney Exchange, QJE '04.
- Roth/Sönmez/Ünver, Pairwise Kidney Exchange, JET '05.
- Ashlagi/Fischer/Kash/Procaccia, Mix and Match: A Strategyproof Mechanism for Multi-Hospital Kidney Exchange, EC '10.
- AGT book, Section 10.4.

**Lecture 11 (Mon 10/28):**Nonatomic selfish routing and the price of anarchy: examples, preliminaries, and tight bounds for all classes of cost functions. Readings:- AGT book, Sections 17.1-17.2.1 and 18.1-18.3.1, 18.4.1.
- For much more on this topic, see the book on Selfish Routing and the Price of Anarchy, MIT Press, 2005, or the "reader's digest" version here.

**Lecture 12 (Wed 10/30):**Case study: network over-provisioning. A bicriteria bound for nonatomic routing networks. POA bounds for atomic routing networks. Readings:- AGT book, Sections 18.3.2, 18.4.2, and 18.5.2.

**Lecture 13 (Mon 11/4):**Potential functions and the existence of pure Nash equilibria. A hierarchy of equilibrium concepts: mixed-strategy Nash, correlated, and coarse correalted equilibria. Readings:- AGT book, Sections 1.3.4, 1.3.6, 19.3.1, 19.3.2.
- T. Roughgarden, Intrinsic Robustness of the Price of Anarchy, STOC '09, Sections 1.1 and 3.1.

**Lecture 14 (Wed 11/6):**Vetta's location games. Smooth games. POA bounds for coarse correlated equilibria and approximate Nash equilibria.- AGT book, Section 19.4.
- T. Roughgarden, Intrinsic Robustness of the Price of Anarchy, STOC '09, Sections 2.1, 2.2, 2.3, 3.1, and 4.1.

**Lecture 15 (Mon 11/11):**Positive externalities and network cost-sharing games. The price of stability. Strong Nash equilibria and their inefficiency.- AGT book, Sections 17.2.2 and 19.3.
- A. Epstein, M. Feldman, and Y. Mansour, Strong Equilibrium in Cost Sharing Connection Games, EC '07.

**Lecture 16 (Wed 11/13):**Best-response dynamics in potential games. Fast convergence to approximate Nash equilibria in symmetric routing games. Fast convergence to near-optimal solutions in smooth potential games.- AGT book, Section 19.3.
- Chien/Sinclair, Convergence to approximate Nash equilibria in congestion games, SODA '07.
- T. Roughgarden, Intrinsic Robustness of the Price of Anarchy, STOC '09, Section 4.3.

**Lecture 17 (Mon 11/18):**Regret minimization. The multiplicative weights (or randomized weighted majority) algorithm. Connection to learning coarse correlated equilbria.- AGT book, Sections 4.1-4.3.
- Lecture notes by Bobby Kleinberg.

**Lecture 18 (Wed 11/20):**Black-box reduction from swap regret minimization to external regret minimization. Connection to learning correlated equilbria. The minimax theorem for two-player zero sum games.- AGT book, Sections 4.4-4.5.

**Lecture 19 (Mon 12/2):**PLS-completeness and negative convergence results for pure Nash equilibria in routing and congestion games. Primary reference:- Section 3 of Roughgarden,
*Computing Equilibria: A Computational Complexity Perspective*.

- Voecking, Congestion Games: Optimization in Competition (Survey Paper), ACiD '06.
- Yannakakis, Chapter 2 in
*Local Search in Combinatorial Optimization*(Wiley, 1997; and Princeton, 2003).

- Section 3 of Roughgarden,
**Lec 20 (Wed 12/4):**PPAD-completeness of computing mixed-strategy Nash equilibria of bimatrix games. Primary references:- Section 4 of Roughgarden,
*Computing Equilibria: A Computational Complexity Perspective*. - AGT book, Sections 2.1-2.6.
- Johnson, Finding Needles in Haystacks, ACM Transacations on Algorithms, 2007.
- Yannakakis, Equilibria, Fixed Points, and Complexity Classes, survey in STACS '08.

- Section 4 of Roughgarden,