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

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 (Physics)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

JACs code: L110

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

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

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 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

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

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.