Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-52-13-M-7

Algorithmic Game Theory (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-52-13-M-7 Algorithmic Game Theory 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-OPT] Optimisation
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-52-13-K-7
Algorithmic Game Theory
P 84 h 186 h - - PL1 9.0 irreg.
  • About [MAT-52-13-K-7]: Title: "Algorithmic Game Theory"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86135 ("Algorithmic Game Theory")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Cooperative Game Theory:
  • games in characteristic function form,
  • solution concepts, e.g. core, Shapley value,
  • complexity of the computation of solution concepts,
  • cost allocation problems,
  • application, e.g. optimization problems in multi-player-situations.

Non-cooperative Game Theory:

  • equilibria, e.g. Nash Equilibria, dominant strategies,
  • complexity of the computation of equilibria,
  • introduction to mechanism design, e.g. truthful mechanisms.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand different solution concepts of the cooperative and non-cooperative game theory. They are able to evaluate the complexity of the solutions of cooperative and non-cooperative games and can find solutions with the help of optimization methods. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements. They are able to analyze the algorithms and apply them to solve practical problems.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.

Literature

  • N. Nisan, T. Roughgarden, E. Tardos, V. Vazirani: Algorithmic Game Theory,
  • M. J. Osborne, A. Rubinstein: A Course in Game Theory,
  • G. Owen: Game Theory.

References to Module / Module Number [MAT-52-13-M-7]

Module-Pool Name
[MAT-52-MPOOL-7] Specialisation Mathematical Optimisation (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)