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MATH20270

Academic Year 2024/2025

Theory of Games (MATH20270)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Assoc Professor Mark Dukes
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

Game Theory seeks to divine an optimum strategy for a person (or company) competing with others who are also seeking an optimum strategy. In this broad sense, game theory attempts to rationalise decision making in diverse areas such as science, business and human interaction.This module will be an introduction to some of the simpler models upon which game theory is based. It will concentrate on strategic games and cover the principle of equilibrium (where parties continue to follow a strategy even though that strategy is known to competitors) for zero sum games. Here von Neumann's minimax theorem applies and guarantees the existence of a game value and equilibrium strategies. We also consider Nash equilibrium for general games, the existence of such equilibria (as proved by Nash) and the search for them. Some topics in combinatorial game theory will also be covered if time permits.

This module will be of interest and relevance to students in a broad range of disciplines. It is quite self-contained but see recommended/required prerequisites.

***If time permits, there will be a midterm exam counting for 20% of the final grade (the remaining 80% being provided by the end of Trimester exam).***

About this Module

Learning Outcomes:

The successful student will be able to
- describe a mathematical model for simple two player games
- choose the optimum strategy for players of a zero sum game
- give examples of the use of game theory in the social, biological and political sciences
- calculate Nash equilibria for strategic games in normal form
- explain the contributions of von Neumann and Nash to the theory of games

Student Effort Hours:
Student Effort Type Hours
Lectures

24
Tutorial

8
Specified Learning Activities

24
Autonomous Student Learning

48
Total

104

Approaches to Teaching and Learning:
Lectures; Tutorials

Requirements, Exclusions and Recommendations
Learning Requirements:

Basic linear algebra (up to eigenvectors)
Caclulus of several real variables (gradient, Hessian matrix, saddle points)
Probability (expectation of a discrete random variable)

Learning Recommendations:

Analysis (continuity/compactness in R^n)


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Midterm Week 7 Alternative linear conversion grade scale 40% No
15
 No
Exam (In-person): End of term exam End of trimester
Duration:
2 hr(s)
 Alternative linear conversion grade scale 40% No
85
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 13:00 - 13:50
Spring Tutorial Offering 1 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 11:00 - 11:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 13:00 - 13:50
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