An Introduction to Linear Programming and Game Theory

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Leader

Mr Carpenter

Cohort

Max 18 Students

Timing

Thursday 6pm

Course Overview

This 8-week short course provides an engaging introduction to Linear Programming and Game Theory, two powerful branches of mathematics used to solve decision-making and optimisation problems. Students will learn how to model real-world scenarios, identify optimal solutions under constraints, and analyse strategic interactions between individuals, businesses, or organisations. Through a combination of practical examples, problem-solving activities, and mathematical techniques, the course explores applications ranging from resource allocation and scheduling to competitive strategy and economics. By the end of the programme, students will have developed valuable analytical skills and a deeper appreciation of how mathematics can be used to make smarter, more effective decisions in complex situations.

Key Benefits

  • Learn powerful optimisation techniques that can be applied to real-world problems involving resource allocation, scheduling, logistics, and planning.
  • Develop strategic decision-making skills by exploring game theory and understanding how outcomes are influenced by the choices of multiple decision-makers.
  • Strengthen mathematical modelling and analytical thinking, enabling students to translate complex scenarios into structured mathematical problems.
  • Gain insight into university-level mathematics and economics concepts, providing excellent preparation for further study in mathematics, business, economics, data science, and related fields.

Course Structure

TBC

Indicative Session Outline

  1. What are algorithms? An introduction to understanding and using some basic algorithms.
  2. Linear programming (part 1). How to formulate a problem in terms of linear programming and illustrate this graphically.
  3. Linear programming (part 2). How to locate the optimal point in a linear programming problem using various methods.
  4. The simplex algorithm (part 1). How to understand and use slack and surplus variables and use simple tableau methods.
  5. The simplex algorithm (part 2). How to use the two-stage simplex method and the Big-M method for maximising and minimising problems
  6. Game theory (part 1). Play safe strategies, stable solutions and reducing the pay-off matrix.
  7. Game theory (part 2). Exploring optimal strategies for games with no stable solution and converting games to linear programming problems.
  8. Game theory in action. A chance to play some simple games and use what you have learnt from the course to calculate optimal strategies.