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 Prisoner’s 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

Assessment

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

Conveners

View in Curriculum Catalogue
Last updated 07/01/2025.