Highgrove Education

Game Theory

In this elective you will be introduced to Game Theory, a branch of Mathematics concerned with strategy. There are players who can choose between certain actions, and their strategies depend on the payoffs of these actions. We’ll consider the classic example: the prisoner’s dilemma, and see how the ideas can be developed further by consideration of iterated elimination of strictly dominated strategies. We’ll then consider the mathematical analysis of zero-sum games. We will consider payoff matrices, play-safe strategies, saddle points, dominance and mixed strategy games. To illustrate the mathematical analysis, we will also play some games and discuss their strategy. To round up the course you will select from a series of topics relevant to game theory and present your findings to the class.

Private Tuition

Key Information

COURSE SYLLABUS

TEACHER PROFILE

Access Course Enrolment:
  • Enrolment in our pre-GCSE or pre-A level access course.
  • Access to our self-study materials and platform, live class lessons, and individual teacher support in Office Hours.
  • Weekly teacher-marked homework.
  • Half termly reports.
  • Support from our SENDCo for pupils with special educational needs or disabilities, including assessment for access arrangement entitlement.
  • Support with English for pupils whose first language is not English.
  • A Highgrove Education Office365 account, including Teams, SharePoint and a school email
DepartmentMathematics
TeacherMr Harry Williams, Head of Mathematics
Course Length10 weeks
Live LessonsOne 45-minute lesson per week
HomeworkStudents will prepare presentation on their chosen area of game theory to be delivered in the final week of the elective.
ExaminationNone 
Entry RequirementsStudents must be studying for GCSEs. This elective is particularly useful for those interested in studying Maths or Economics A level.

Course Syllabus

Lesson 1Introduction to Game Theory – players, actions, payoffs
Lesson 2The Prisoner’s Dilemma
Lesson 3Student presentation topic selection and preparation
Lesson 4Applications and further development of the Prisoner’s Dilemma
Lesson 5Iterated elimination of strictly dominated strategies
Lesson 6Further examples of iterated elimination of strictly dominated strategies 
Lesson 7Introduction to zero sum games: rock, paper, scissors (lizard, spock)
Lesson 8Zero sum games
Lesson 9Student presentation preparation
Lesson 10Student presentations

Teacher Profile

Mr Williams has taught Maths and Further Maths for over ten years prior to joining Highgrove Education, most recently at Harrow School Online, where in 2023 his pupils achieved 90% A*-A in Maths and 100% A*-A in Further Maths. Before this he taught at Abingdon School where he was responsible for their UKMT challenges and Sixth Form Maths Enrichment. Mr Williams graduated with a First class Masters degree in Mathematics from the University of Sussex in 2013, then went on to complete his PGCE with the University of Reading. He is a keen advocate for the power of technology to enhance and indeed transform pupils’ enjoyment and understanding of Mathematics.