Game Theory
| Code | School | Level | Credits | Semesters |
| MATH3053 | School of Mathematical Sciences | 3 | 10 | Spring China |
- Code
- MATH3053
- School
- School of Mathematical Sciences
- Level
- 3
- Credits
- 10
- Semesters
- Spring China
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 Honours students from the School of Mathematical Sciences who have successfully completed Part I.
Classes
- One 2-hour lecture each week for 12 weeks
Assessment
- 100% Exam 1 (2-hour): 2 hours written exam
Assessed by end of spring semester
Educational Aims
The purpose of this course 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. This course 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.