Game Theory

Manuscript and lectures (as videos) by Prof. Dr. C. Hertling.
Exercises as Zoom sessions by K. Larabi, additional optional exercises in presence by M. Vujic.
Manuscript + videos on it and the 11 exercise sheets are on the ILIAS acount of the course. Participants should enroll there.

Manuscript and Lectures

A manuscript is available on the ILIAS account of the course.

Lectures will be recorded as youtube videos. They will be available in the teaching time of the HWS 2020 on the youtube channel Mathe Mannheim and also on ILIAS. The list below is ordered by number of week and exercise sheet. The videos from week „n“ should be studied before working on sheet „n“. For example, the numbers 2.1-2.4 mean Definition 2.1 - Notations 2.4.

Week 1, Sheet 1, 29.09.2020: 2.1-2.4, 2.5-2.9, 2.10-2.11, 2.12-2.13.
Week 2, Sheet 2, 06.10.2020: 2.14-2.17, 2.18-2.19, 2.20-2.22, 2.23-2.27, 2.28-2.29, 2.30-2.31.
Week 3, Sheet 3, 13.10.2020: 2.32-2.34, 2.35-2.36, 2.37, 2.38-2.40, 2.41-2.42, 3.1-3.4.
Week 4, Sheet 4, 20.10.2020: 3.5-3.7 (without proof of 3.6), proof of 3.6+3.8+3.9(a), 3.9(b)+2nd proof of 3.3, 3.11+3.12(a)(b)(c), 3.12(d)+3.13.
Week 5, Sheet 5, 27.10.2020: 3.12(e)(f)+3.16, 3.12(e)+3.14+3.15, 3.17-3.19, 3.20-3.21.
Week 6, Sheet 6, 03.11.2020: 4.1-4.4, 4.5-4.6, 4.7-4.9, 4.10-4.11.
Week 7, Sheet 7, 10.11.2020: 5.1-5.6, 5.7-5.8, 5.9-5.10, 5.11-5.14(without proof).
Week 8, Sheet 8, 17.11.2020: Proof of 5.14, 5-15-5.17, 5.18-5.19, 5.20-5.21(ii), 5.21(iii)-5.22.
Week 9, Sheet 9, 24.11.2020: 5.23-5.25, 5.26-5.28, 5.29-5.31, 5.32-5.34, 5.35-5.36.
Week 10, Sheet 10, 01.12.2020: 5.37+5.38(with part of proof)+5.39, 5.40, 5.38 (rest of proof)+5.41, 6.1-6.3, 6.4-6.10.
Week 11, Sheet 11, 08.12.2020: 6.11-6.12, 6.13-6.15, 6.16-6.17, proof of 6.10+6.18, 6.19-6.22, 6.23-6.26(without proof).
Week 12, 15.12.2020: Proof of 6.26(a)(b)(c), proof of 6.26(d)(e)(f)-6.28.

Exercise sessions

Exercises as Zoom sessions: K. Larabi, Tuesday 13:45-15:15, from 06.10. until 15.12.2020. The solutions to the weekly exercises will be explained in these exercises. The Zoom room is WIM-ZOOM-01. The link can be found on the Portal2 (MAB 506 Game theory, Termine&Räume, 1.PG).

Additional optional exercises in presence at the University (if possible: yes in October, no in November and  December): M. Vujic, Thursday 13:45-15:15, from 01.10. until end of October. Room: 209, B6, Bauteil E („Corona-Gebäude“).

Exam

The exam is a written exam. The 1st exam was on 16 January 2021. For participation in the exam, one has to reach half of the points in the exercises. The date of the 2nd exam is presumably 26 February 2021. Since 01.12.2020, 4 old exams (from 2012, 2015, 2016, 2017) are in the folder „exercises“ on ILIAS (between the solutions and the exercises. 16.01.2021: The grades of the 1st exam are now on the portal. In the folder „exercises“ on ILIAS are now also the following 2 files: the 1st exam with solutions, the translation points->grade. Here is a link to Prüfungs-ILIAS, where each participant of the 1st exam can look at the scanned version of his corrected exam. If somebody thinks that he/she deserves more points and a better grade, please write an email to Prof. Hertling.

Exercises

On each Tuesday from 29.09.2020 to 08.12.2020, there will be a new sheet of exercises on ILIAS (a list of the dates and numbers of the sheets is above). All participants are advised to work out the exercises. They are integral part of the course. They complement the lectures by giving examples, and they give the chance to work yourself through typical arguments.
There will be 11 sheets altogether. Each will be worth 16 points. Up to two people can submit solutions together, until Tuesday at 11:50 one week later, via ILIAS. Official solutions will be discussed on the same Tuesday at 13:45-15:15. The students' solutions will be graded as fast as possible; feedback will be given via ILIAS.
In order to be allowed to take part in the exam, one has to reach 11 times 8 = 88 points in the exercises.

Literature

There are many good books on game theory. The book of von Neumann and Morgenstern founded game theory. The other books listed had been useful in preparing the course.

Walter Schlee: Einführung in die Spieltheorie. Mit Beispielen und Aufgaben. Vieweg Verlag, 2004.

Ken Binmore: Game theory. A very short introduction. Oxford University Press, 2007.

J. Gonzalez-Diaz, I. Garcia-Jurado, M.G. Fiestras-Janeiro: An introductory course on mathematical game theory. Graduate Studies in Mathematics vol. 115, AMS, 2010.

John von Neumann, Oskar Morgenstern: Theory of games and economic behaviour. Princeton University Press, 1944.

Manfred J. Holler, Gerhard Illing: Einführung in die Spieltheorie. Springer Verlag, 2006 (6. Auflage).

Siegfried K. Berninghaus, Karl-Martin Ehrhart, Werner Güth: Strategische Spiele. Springer Verlag, 2010 (3. Auflage).