# GAME THEORY WITH APPLICATIONS IN ECONOMICS AND BIOLOGY - 2021/2

Module code: MAT3046

## Module Overview

This module introduces the topic of Game Theory and various mathematical techniques used in the analysis of games. Classic examples of games are introduced including those with application in economics and biology. The theoretical backbone is a combination of Calculus, Linear Algebra, Ordinary Differential Equations and, in the case of mixed strategies for games, Probability.

### Module provider

Mathematics

SKELDON Anne (Physics)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 104

Seminar Hours: 13

Guided Learning: 11

Captured Content: 22

Semester 2

NONE.

## Module content

Indicative content includes:

• Combinatorial games

• Extensive games

• Zero sum games

• General sum games such as the Prisoner’s Dilemma and the Public Goods Game.

• Evolutionary games

• The Kuhn-Tuckeer-Karush Theorem

• Application of Brouwer's Fixed-Point Theorem.

## Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test Online Test 20
Examination Online Online Exam 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Subject knowledge through explicit and implicit recall of key definitions and theorems as well as interpreting this theory.

• Understanding and application of subject knowledge to solve constrained optimization problems, originating from two-player zero-sum/constant-sum/general-sum games, including repeated and evolutionary games

Thus, the summative assessment for this module consists of:

• One two-hour examination (three answers from four contribute to exam mark) at the end of the semester; worth 80% of module mark.

• One in-semester test; worth 20% of module mark.

Formative assessment and feedback

Students receive individual written feedback via a number of marked formative coursework assignments over an 11-week period.  The lecturer also provides verbal group feedback during lectures.  (Occasionally group feedback may be provided online when applicable.)

## Module aims

• Introduce students tothe way that decisions and strategyies can be framed in the language of Game Theory.
• Illustrate key concepts of introductory Game Theory by considering combinatorial games, two-player zero-sum/constant-sum/general-sum games. Enable students to solve such game-based problems.
• Enable students to solve nonlinear programming problems in the context of Game Theory using the Kuhn-Tucker-Karush Theory and duality.
• Introduce students to Evolutionary Game Theory and techniques for analysing evolutionary games.

## Learning outcomes

 Attributes Developed 001 Understand the basic principles of Game Theory K 002 Formulate static games in either combinatorial, extensive or matrix form and understand how to analyse them to find optimal strategies KC 003 Formulate strategy matrices as linear programming problems and solve these problems by choosing a suitable method, including understanding how to apply the Kuhn-Tucker-Karush Theory where appropriate KC 004 Recall supporting theory for solving general-sum games and apply fixed-point theory to show existence of equilibria KC 005 Understand how to analyse repeated games KC 006 Understand how to analyse evolutionary games KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Give a detailed introduction to Game Theory, which requires understanding and studying a range of mathematical techniques, including methods of solution for nonlinear programming problems.

• Ensure experience is gained (through demonstration) of the methods typically used to formulate and solve game theory problems so that students can later apply their own decision-making to formulate and solve game theoretic problems.

The learning and teaching methods include:

3 x 1 hour lectures per week for 11 weeks, including notes plus extra examples written and worked through on the board (or projector-display) .  This also includes Q&A opportunities for students.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT3046

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 2 Optional A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module
Mathematics and Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2021/2 academic year.