Game Theory
| Code | School | Level | Credits | Semesters |
| MATH3004 | Mathematical Sciences | 3 | 10 | Spring UK |
- Code
- MATH3004
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 10
- Semesters
- Spring UK
Summary
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The course starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoners Dilemma. We look at tree-searching, including alpha-beta pruning, the killer heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Target Students
Single and Joint Honours students from the School of Mathematical Sciences who have successfully completed Part I. Available to MSc Financial Mathematics, Natural Sciences, Liberal Arts students.
Classes
- Two 1-hour lectures each week for 10 weeks
Assessment
- 100% Exam 1 (2-hour): Written examination.
Assessed by end of spring semester
Educational Aims
The purpose of thiscourse is to show how games can be analysed, by computer and otherwise; how games can be related to numbers; the theory of a representative collections of (mathematical games); and how new games can be investigated and are related to other games. Thiscourse will broaden the students experience of using mathematics to analyse various situations in a logical manner. It will enable students to analyse familiar and unfamiliar situations in other areas of mathematics and elsewhere, where strategic decision-making is required.Learning Outcomes
L1 – Find Nash equilibria and Pareto optima of games
L2 – Construct and analyse games in extensive form, and apply alpha-beta pruning to game trees
L3 – Understand the connection between combinatorial games and numbers, and determine the value of a game
L4 – Find the Nim values of impartial games
L5 – Analyse the properties of voting systems, and understand which of these properties are mutually exclusive