Algorithmic Game Theory, Autumn Semester 2020
Short Course Description
provides a good model for the behavior and interaction of rational/selfish agents and
programs in large-scale distributed systems without central control.
The course discusses algorithmic aspects of game theory, such as a general
introduction to game theory, auctions, mechanisms, the costs of a central
control optimum versus those of an equilibrium under selfish agents, and
algorithms and complexity of computing equilibria.
The ETHZ Course Catalogue information can be found here.
Time and Place
First lecture 21 Sept, first Exercise Class 22 Sept.
|Exercise Class (Group 1)
|Exercise Class (Group 2)
|Exercise Class (Group 3)
Starting from Nov 2, lectures and exercise classes are on Zoom (details in Piazza).
Lectures are live-streamed
Recordings will appear online after 24 hours.
Note (exercise class groups):
Students are divided into the three groups according to the family name
Group 1 = A-He;
Group 2 = Hi-M;
Group 3 = N-Z.
Moving to another group is only possible in special cases, after the instructor approval, and according to the current ETH measures/rules. Priority will be given to students who have conflicts with other lectures. Students who need to be moved to a different group should contact Stanislas Gal
. Due to restricted rooms occupancy, an online exercise session
may also be offered on Zoom (details in Piazza
Some Slides (organization, grading and exercises, course intro)
- Games in strategic form and equilibrium concepts (pure, mixed, dominant strategies,...).
- Existence and computation of equilibria (potential games, complexity of
computing Nash equilibria, regret minimization algorithm,...).
Inefficiency of equilibria (Price of Anarchy, Price of Stability, analysis via the smoothness framework,...).
- Mechanism design (with and without money). Single-item auctions, first-price and Vickrey auction, characterizations of
truthful mechanisms, applications, and complexity. Mechanisms without money, limitations of general voting schemes, constructions of incentive compatible mechanisms.
Material and Literature
There will be lecture notes for the
course. Taking your own notes is advisable. Some of the material presented in
the lecture can be found in the following book:
- [ROU] Twenty Lectures on Algorithmic Game Theory, Tim Roughgarden, Cambridge University Press, 2016.
(The book is available in the computer science library.)
Further books containing additional material:
- [AGT] Algorithmic Game Theory, edited by N.
Nisan, T. Roughgarden, E. Tardos, and V. Vazirani, Cambridge University Press,
- [GTS] Game Theory and Strategy, Philip
D. Straffin, The Mathematical Association of America, fifth printing, 2004.
(A gentle introduction to the basic concepts of game theory. The book is available in the computer
- [NCM] Networks, Crowds, and Markets, David Easley and Jon Kleinberg, Cambridge University Press, 2010.
(An online draft is available)
- ... more will be added.
Weekly exercise assignments will be published on this web page (shortly after each lecture). You are encouraged to hand in solutions to the
problems on Monday during the (following) lecture. The (handed in) solutions will be looked at and
returned with comments in the subsequent week.
There will be four graded exercise sheets that will contribute with a
weight of 30% towards the final grade. The graded exercise sheets will be every third lecture (weeks 3, 6, 9, 12), and the best 3 of them will determine your "excercise grade".
There will be a written exam
in the exam session. The exact date will be announced later by the examination
office. It will take 3 hours and will be a closed-book examination.
Your final grade will be calculated as the weighted average of the
final written exam (weight 70%) and of the graded exercise sheets (weight
Following the new D-INFK guidelines for doctoral studies, PhD
students get credit points according to the same rules that apply for Bachelor
or Master students. That is, with a final grade of at least 4 doctoral students
will receive 7KE, and 0KE otherwise.
Frequently Asked Questions
the meaning of "sixth hour" and "seventh credit point" in
the Course Catalogue?
Apart from the three hours of regular lectures (V) and two hours of
exercises (U), this course comes with one extra hour of independent work
(A); this makes 7 credit points. You will deserve the credits for the A-unit by
independent work, i.e. studying and learning material (also prerequisites) on
your own. Details will be announced at the beginning of the course the
A tentative program:
Introduction and motivations
- Strategic games and existence of (pure Nash) equilibria.
- Best-response dynamics (convergence in potential games).
- Congestion games (and the restriction to singleton congestion games).
|Strategic games, equilibria, congestion games
||Exercise set 1
Efficiency and computation of equilibria
- Price of anarchy, smooth framework, affine congestion games.
- An efficient algorithm for symmetric network congestion games.
|Price of anarchy and hardness of equilibria
(Sect. 2.2-2.4 next week)
|Exercise set 2
More general equilibria and computation
- Hardness of pure Nash equilibria (polynomial local search, PLS-reductions, max-cut game, congestion games are PLS-complete)
- Mixed and (coarse) correlated equilibria.
- Price of anarchy for these equilibria via the smooth framework.
|Mixed and correlated equilibria
(plus Sect. 2.2-2.4 in lecture notes 2)
|Exercise set 3
Efficient computation of correlated equilibria.
- Regret minimization algorithm (multiplicative weights update).
- From regret-minimization to correlated equilibria.
| Regret minimization and correlated equilibria
(Section 2 next week)
|Exercise set 4
Price of Stability. Mechanisms with money
- Price of Stability (fair cost sharing games, tight bound).
- Truthful mechanisms (2nd price auction, shortest path, truthfulness).
| Price of Stability and Introduction to Mechanism Design
(until Section 2.1)
|Exercise set 5
Two constructions of truthful mechanisms
- VCG mechanisms.
- One-parameter mechanisms (monotone algorithms, truthfulness).
- Examples of impossibility results.
| Truthful one-parameter mechanisms
(plus Sect 2.2 - 2.4 in lecture notes 5; Section 3 next week)
|Exercise set 6
Truthful mechanisms and approximation
- Combinatorial auction (general setting and single minded bidders).
- VCG mechanisms, one-parameter, monotonicity and threshold payments.
- Two simple optimal mechanisms (greedy for single minded).
| Incentives vs Computation
(plus Sect 3 in lecture notes 6)
|Exercise set 7
Mechanisms without money
- Voting systems, basic definitions (social welfare functions, social choice functions).
- Two alternatives vs many alternatives (tournament voting, majority, positional voting).
- Arrow's impossibility result, Gibbard-Satterthwaite Theorem.
- Single-peaked preferences and median voting.
(for single-peaked prefs: Chapter 10 in [AGT] or Chapter 23 of [NCM].)
|Exercise set 8
Mechanisms without money II
- Arrow's Theorem (proof).
- House Allocation (TTCA Algorithm, core allocation).
|Mechanism Design Without Money II
(proof Arrow's Theorem in previous lecture notes)
|Exercise set 9
Mechanisms without Money II (contd)
- Kidney Exchange (setting, TTCA vs Maximal Matching mechanism).
- Stable Matching.
- Instability of "BGP" and best-response (introduction).
|Mechanism Design Without Money II
||Exercise set 10
- Asynchronous best-response for distributed settings.
- The BGP game.
- Sufficient conditions for convergence and incentive compatibility.
- The Gao-Rexford Model for BGP.
|Best response mechanisms
(Section 3.4 next week)
|Exercise set 11
Best-response mechanisms II
- Application to TCP.
- Stable matching mechanisms revisited (proposal mechanism for Interns-Hospitals matching and other restrictions).
- Re-proving incentive compatibility via best-response mechanisms.
- Single-item auction revisited.
|Best-Response Mechanisms II
(Section 1 - see also here for a nice introduction and motivation
|Exercise set 12
Sponsored search auctions
Plus a bonus/fun topic (to be decided)
- Truthful VCG versus GSP used in practice.
- Guarantees of GSP (equilibria characterizations, symmetric equilibria, social welfare and revenue bounds).