Algorithmic Game Theory, Autumn Semester 2021


Paolo Penna


Andrei Ivanov
Lorenzo Laneve
Varun Maram

Short Course Description

Game theory 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.

Some of the applications we shall discuss in the lectures or in the exercises include: BGP and TCP protocols, Google sponsored search, Generative Adversarial Networks, Reinforcement Learning approaches.

The ETHZ Course Catalogue information can be found here.

Time and Place (changed schedule!)

First lecture 27th September 24th September, first Exercise Class 28th September (no exercise class first week).

Type Time Place
Lectures Mon 10-13 Fri 10-13 CAB G51 CHN C14
Exercise Class (Group 1) Tue 10-12 CAB G57
Exercise Class (Group 2) Tue 10-12 CAB G59
Exercise Class (Group 3) Tue 16-18 LFW B3

Note (exercise class groups):

Students are divided into the three groups according to the family name (groups will be announced soon).

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 Varun Maran.



Further Info

Some Slides (organization, grading and exercises, course intro)


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:

Further books containing additional material:


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 30%).

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

What is 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 latest.

A tentative program:

Lecture Topics Lecture Notes Exercise Sheet

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
(Video Recording)
Exercise Set 1

Efficiency and computation of equilibria

  • Price of anarchy, smooth framework, affine congestion games
  • An efficient algorithm for symmetric network congestion games
  • Finding a pure Nash equilibria may be hard
Price of anarchy and Hardness of equilibria - sect 2.2-2.3 next week
(Video Recording)
Exercise Set 2

More general equilibria and computation

  • More general equilibria (mixed and correlated equilibria)
  • Price of anarchy for general equilibria via the smooth framework
Mixed and correlated equilibria
(Video Recording)
Exercise Set 3
(Graded Set)

Efficient computation of correlated equilibria

  • Regret minimization algorithm (multiplicative weights update)
  • From regret-minimization to correlated equilibria
Regret minimization and correlated equilibria
(Video Recording)
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)
  • VCG mechanisms
Price of Stability and Introduction to Mechanism Design - sect 2.4 next week
(Video Recording)
Exercise Set 5

Two constructions of truthful mechanisms

  • Longest path (impossibility result)
  • One-parameter mechanisms (monotone algorithms, truthfulness)
  • More of impossibility results
Truthful One-Parameter Mechanisms
(Video Recording)
Exercise Set 6
(Graded Set)

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 and Computation
(Video Recording)
Exercise Set 7

Mechanisms without money

  • Sequential-Dictator Mechanism
  • House Allocation, Kidney Exchange, Stable Matching
  • Stronger guarantees (coalitions, core, stability)
Mechanisms Without Money - Thm 8.6 and Thm 8.7 (truthfulness) next week
(Video Recording)
Exercise Set 8

Best-response mechanisms

  • Best-response in (asynchronous) distributed settings
  • Instability of "BGP" and best-response.
  • Convergence and incentive compatibility
and more mechanisms without money (single-peaked domains)
Best response mechanisms - from Def 7 onwards next week,
Single peaked domains - in AGT book
(Video Recording)
Exercise Set 9
(Graded Set)

Best-response mechanisms II

  • Convergence and incentive compatibility
  • The real BGP and the TCP protocols
  • More applications (stable-matching, interns-hospitals matching, single-item auction)
Best response mechanisms II
(Video Recording)
Exercise Set 10

Sponsored search auctions

  • Theory vs practice (truthful VCG versus GSP)
  • Guarantees of GSP (equilibria characterizations, social welfare and revenue)
Sponsored search and (non-)truthful mechanisms
(Video Recording)
Exercise Set 11

Very easy games (obviously strategyproof)

  • Dominant and obviously dominant strategies
  • Extensive form games (simple examples)
  • Obviously strategyproof mechanisms (with and without money)
Very easy games: Obviously Strategyproof Mechanisms
(Video Recording)
Exercise Set 12
(Graded Set)

Very hard games

  • Generative adversarial networks
  • Extensive form games, repeated games, reinforcement learning methods
Very hard games
(Video Recording)