• 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)

There will be one exercise sheet after every lecture containing G-, H- and T-exercises. Additional Q-exercises will be available in Moodle.

 

• 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 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.

• 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 2019, grades of later exams are not affected.

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 are no "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 need 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.

This course is not based on a textbook. The literature listed below can be helpful to get a better understanding of some concepts, but the notation and terminology might deviate from the lecture.

You might also consult this document by Itzhak Gilboa or this document by Walter Bossert (the latter covers much more than we need in this course). Michael Sipser's book "An Introduction to the Theory of Computation" also contains a good introduction to basic mathmatical notions and proof techniques.