This information is for the 2020/21 session.
Teacher responsible
Prof Bernhard Von Stengel COL 4.12
Availability
This course is available on the BSc in Business Mathematics and Statistics, BSc in Management, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics and Business and BSc in Psychological and Behavioural Science. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
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. Basic knowledge of matrices as covered in Mathematical Methods (MA100) or Quantitative Methods (MA107) as well as some knowledge of probability is required.
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
This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.
Formative coursework
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Lecture notes will be provided. Further reading: K Binmore, Playing for Real: Game Theory, CUP, 2007; E Mendelson, Introducing Game Theory and Its Applications, CRC 2004.
Assessment
Exam (90%, duration: 2 hours) in the summer exam period.
Coursework (10%).
Weekly exercises will be set and marked, and count as coursework.
Key facts
Department: Mathematics
Total students 2019/20: 47
Average class size 2019/20: 15
Capped 2019/20: No
Value: Half Unit
Personal development skills
Important information in response to COVID-19
Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.