Game Theory I

**This information is for the 2019/20 session.**

**Teacher responsible**

Prof Bernhard Von Stengel

**Availability**

This course is available on the CEMS Exchange, MBA Exchange, MSc in Applicable Mathematics, MSc in Financial Mathematics, MSc in Management Science (Decision Sciences) and MSc in Operations Research & Analytics. This course is available as an outside option to students on other programmes where regulations permit.

It is not available to students who have taken Game Theory (MA300) or Game Theory I (MA301).

**Pre-requisites**

The course emphasises a formal treatment of mathematical Game Theory through definitions, theorems and proofs. Familiarity with a rigorous treatment of mathematics is expected. Students must know basics of linear algebra (matrix multiplication, geometric interpretation of vectors) and probability theory (expected value, conditional probability, independence of random events).

**Course content**

Concepts and methods of mathematical game theory with some applications to economics. Nim and combinatorial games. Congestion games. Game trees with perfect information. Backward induction. Extensive and strategic (normal) form of a game. Expected utility. Nash equilibrium. Commitment. Zero sum games, mixed strategies, maxmin strategies. Nash equilibria in mixed strategies. Finding mixed-strategy equilibria for two-person games. Extensive games with information sets, behaviour strategies, perfect recall. If time permits: The Nash bargaining solution, multistage bargaining, private-value auctions.

**Teaching**

20 hours of lectures and 10 hours of seminars in the MT. 2 hours of lectures in the ST.

**Formative coursework**

Weekly exercises are set and marked.

**Indicative reading**

Lecture notes will be provided. Supplementary reading: K Binmore, Playing for Real: Game Theory CUP, 2007; E Mendelson, Introducing Game Theory and Its Applications, CRC 2004

**Assessment**

Exam (100%, duration: 2 hours) in the summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 27

Average class size 2018/19: 15

Controlled access 2018/19: No

Value: Half Unit

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills