AØKA08076U Game Theory
This is a mathematically oriented course of game theory.
The course covers the standard parts of game theory, focusing mainly on non-cooperative games. The course starts with the expected utility theorem. For non-cooperative games, the teaching covers the most important solution concepts for strategic and extensive form games as well as some refinements of those solution concepts. The Aumann model of knowledge is presented. Also, the theory of games under uncertainty is discussed, leading to the extension of the solution concepts previously encountered. We will apply these solution concepts in implementation and mechanism design problems. The course also gives an introduction to matching problems.
We will formally show under which assumptions the covered solution concepts exist and derive certain properties. We will then illustrate and apply the solution concepts in examples and exercises.
The course aims at giving the students the abilities and competences needed to understand and assess the fundamental aspects of strategic decision making by rational individuals where the framework for decision making specifies the actions open to the individuals as well as their objectives and the information available. Methodologically, the course will get students more accustomed to formal notation and proofs. More specifically, the students are expected to have the following competences at the end of the course:
Knowing and assessing the basic components of a game and their formal representation,
Knowledge of solution concepts (and refinements) for specific forms of non-cooperative games as well as the ability to find solutions in fully specified games,
Understanding the importance of the structure of a game for the solution, and knowledge of the restriction of solutions derived from considerations regarding unrealistic threats.
Knowing the approach to games under uncertainty and the solution concepts arising as a consequence of this approach,
Familiarity with the idea of (common) knowledge and its formalization
Knowledge of implementation of decision rules in several solution concepts and of the basic notions of mechanism design
Knowledge of the core as solution concept for cooperative games and the Gale-Shapley algorithm for matching problems.
Martin J. Osborne and Ariel Rubinstein: “A Course in Game Theory”, MIT Press, 1994 (note that an electronic version of the book is available for free from the websites of the authors);
M. Maschler, E. Solan and S. Zamir: “Game Theory”, Cambridge University Press, 2013
the text books will be supplemented by some papers assigned during the lectures
Other useful sources:
Drew Fudenberg and Jean Tirole: “Game Theory”, MIT Press, 1991
Mas Colell, Whinston , Greene: “Microeconomic Theory”, Oxford University Press, 1995
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilationA 3 hours written examination taking place at Peter Bangs Vej 36.
- Exam registration requirements
- One written take home assignment must be approved for students to be able to take the exam.
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
100 % censurship
- Exam period
- Will be updated before the start of the semester
- Same as ordinary. But if only a few students have registered for the re-exam, the exam might change to an oral exams with a synopsis to be handed in. This means that the examination date also will change.
Criteria for exam assesment
- Theory exercises