# GAME THEORY WITH APPLICATIONS IN ECONOMICS AND BIOLOGY - 2023/4

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

### Module Leader

SKELDON Anne (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 6

### JACs code: L110

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

## Overall student workload

Independent Learning Hours: 84

Lecture Hours: 33

Captured Content: 33

## Module Availability

Semester 2

## Prerequisites / Co-requisites

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 |
---|---|---|

School-timetabled exam/test | In-semester test (50 min) | 20 |

Examination | Exam (2 hrs) | 80 |

## Alternative Assessment

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 final examination, worth 80% of the 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.

## 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.

## Reading list

https://readinglists.surrey.ac.uk

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 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 |

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 |

Mathematics with Music BSc (Hons) | 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 |

Financial Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematical Data Science MSc | 2 | Optional | A weighted aggregate mark of 50% 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 2023/4 academic year.