# MATH20270 Theory of Games

## Academic Year 2023/2024

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).***

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Curricular information is subject to change

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 Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Class Test: Midterm class test to happen close to the 2 week study period Throughout the Trimester n/a Alternative linear conversion grade scale 40% No

15

No
Examination: End of Semester exam 2 hour End of Trimester Exam No Alternative linear conversion grade scale 40% No

85

No

Carry forward of passed components
No

Resit In Terminal Exam
Autumn Yes - 2 Hour