Prof. Dr. Felix Brandt, M.Sc. Johannes Hofbauer, and M.Sc. Christian Saile

**Lecture and Tutorials in SS2018**

## Algorithmic Game Theory (IN2239)

### Organization

**Lecture:**Tuesdays 15.00 - 16.30, Interims HS 1 (5620.01.101) (first lecture on April 09)**Tutorials:**(registration opens on April 09, 2018, 20.00 via TUMonline; first tutorials on April 16 and 17, respectively)**Group 1:**Mondays 10.15 - 11.45, 01.10.011**Group 2:**Mondays 17.15 - 18.45, 01.10.011**Group 3:**Tuesdays 12.00 - 13.30, 01.10.011

**SWS:**2+2**Credits:**5**Classification:**"Formale Methoden und ihre Anwendungen" (FMA)**Module description:**IN2239**Language:**English**Office hours:**by arrangement**Exam:**tba**Exam registration:**tba (via TUMonline)

**theory course**. It is expected that participants are familiar with formal mathematics, concepts such as continuity or convexity, and standard proof techniques. Additionally, basic knowledge about NP-completeness and linear programming is useful.

### Content

Algorithmic game theory is a young research area at the intersection of theoretical computer science, mathematics, and economics that deals with the optimal strategic behavior in interactive situations. In this course, particular attention will be paid to algorithmic aspects of game-theoretic solution concepts such as Nash equilibrium and the abstract design of economic mechanisms. The concrete design of specific mechanisms for resource allocation (auctions) and collective choice (voting rules) is covered by the courses Auction Theory and Market Design and Computational Social Choice, respectively.

#### Tentative list of topics:

- Utility theory (preference relations, expected utility, von Neumann-Morgenstern preferences)
- Normal-form games (prisoner's dilemma, Pareto-dominance, dominance)
- Nash equilibrium (pure and mixed equilibria, axiomatization)
- Computing equilibria (hardness, support enumeration, zero-sum games, minimax theorem, linear programming)
- Alternative solution concepts (equilibrium refinements, Shapley's saddle)
- Concise representations (graphical games, anonymous games)
- Extensive-form games (subgame-perfect equilibria)
- Mechanism design (Gibbard-Satterthwaite impossibility, Nash implementation, quasi-linear preferences, VCG mechanism)
- Cooperative games (Shapley value, coalition formation)
- Stable matchings (Gale-Shapley algorithm, hedonic games)

### Exercises

- G(ame)-exercises: Students' answers have to be submitted by midnight (i.e., 23.59) each Saturday before the next tutorial. Results will be presented in the subsequent tutorial. Points earned here can help improve the final grade, please see below for details.
- H(omework)-exercises: Should be prepared before the tutorial and can be handed in on a voluntary basis. Will be discussed in detail in the tutorial. Solution hints will be published online afterwards.
- T(utor)-exercises: Will be presented by the tutor in the tutorial. Solution hints will be published online afterwards. Students are not expected to prepare them beforehand.
- Q(uiz)-exercises: Will be made available and can only be answered online in Moodle once every three to four weeks. Points earned here can help improve the final grade, please see below for details.

**Grade Bonus:**

- At the end of the semester, the points acquired in all G- and Q-exercises will be summed up to form a final score, the theoretical maximum may be well beyond 40. Using the same thresholds as for the exam (see below), this score will be converted to a so-called G-grade.
- Based on APSO Section 6 Subsection 5 (2), this G-grade can only be used to
**improve**the grade of a**passed**exam, i.e., if you pass the exam and your G-grade is better than your exam grade, then your final grade will be computed according to the following formula:

`final_grade = 0.8 * exam_grade + 0.2 * G-grade`

- Note that the bonus only applies to the grades of passed exams.
- Note that grades can only be improved by the bonus, never worsened.
- Note that the bonus only applies to the exam of the summer term 2018, grades of later exams are not affected.

### Slides and exercise sheets

Lecture slides, exercise sheets, and solution hints will only be available in Moodle.

### Exam

There will be a written exam at the end of the semester, which will be graded according to the following grading scale:

- [0,5) points: 5,0
- [5,11) points: 4,7
- [11,17) points: 4,3
- [17,19] points: 4,0
- (19,22] points: 3,7
- (22,24] points: 3,3
- (24,26] points: 3,0
- (26,28] points: 2,7
- (28,30] points: 2,3
- (30,32] points: 2,0
- (32,34] points: 1,7
- (34,36] points: 1,3
- (36,40] points: 1,0

The only resource you may use during the exam is one hand-written sheet of DIN A4 paper that you prepared yourself (you may write on both sides). In particular, electronic devices, books, photocopies, and printouts are disallowed. All content from lecture and tutorials is relevant for the exam. Please remember to bring your student id (or an equivalent photo id).

You will be notified by email when the grades are available in TUMonline.

### On G-exercises

The purpose of G-exercises is to provide additional insight into game-theoretic situations by experiencing them from the perspective of an actual decision maker. Bonus points are used to set up incentives according to the games' payoffs. You will quickly realize that there seldom are "correct" solutions (though there are sometimes particularly poor solutions). In some G-exercises, pairs of players may be randomly matched with each other to play a two-player game. It is therefore possible that two students who submit the same strategy receive different scores because their respective opponents submitted different strategies. This is in the nature of things and you should not worry about this too much. To a large extent, the G-grade is determined by the quizzes. G-exercises can be a lot of fun and we hope you enjoy playing the games.

### Literature

#### Books (available online for free):

- Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay Vazirani:
*Algorithmic Game Theory*(Cambridge University Press, 2007) - Martin Osborne and Ariel Rubinstein:
*A Course in Game Theory*(MIT Press, 1994) - Robert Aumann:
*Game Theory*, in J. Eatwell, M. Milgate, and P. Newman: The New Palgrave, A Dictionary of Economics, Vol. 2 (MacMillan, 1987) - Yoav Shoham, Kevin Leyton-Brown:
*Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations*(Cambridge University Press, 2009)

**Other recommended books:**

- Hans Peters:
*Game Theory - A Multi-leveled Approach*(Springer, 2008) - Michael Maschler, Eilon Solan, and Shmuel Zamir:
*Game Theory*(Cambridge University Press, 2013) - Roger Myerson:
*Game Theory - Analysis of Conflict*(Harvard University Press, 1991) - Drew Fudenberg and Jean Tirole:
*Game Theory*(MIT Press, 1991) - Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green:
*Microeconomic Theory*(Oxford University Press, 1995)