Topic summary · Decision maths (D2)
Game Theory summary
Two-player zero-sum games use payoff matrices, pure and mixed strategies, and expected-value calculations.
Files: D2-Game Theory.pdf · D2-Game Theory answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Row player maximises; column player minimises.
- A saddle point gives a stable pure-strategy solution.
- Mixed strategies equalise the opponent’s expected payoffs.
- The value of the game is the expected payoff under optimal play.
Worked example 1 — Saddle
What is a saddle point in a payoff matrix?
Working
It signals a pure-strategy equilibrium.
Worked example 2 — Row player maximises; column player minimises
Use this method from the Game Theory sheet: Row player maximises; column player minimises.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 3 — A saddle point gives a stable pure-strategy solution
Use this method from the Game Theory sheet: A saddle point gives a stable pure-strategy solution.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 4 — Mixed strategies equalise the opponent’s expected payof
Use this method from the Game Theory sheet: Mixed strategies equalise the opponent’s expected payoffs.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 5 — The value of the game is the expected payoff under opti
Use this method from the Game Theory sheet: The value of the game is the expected payoff under optimal play.
Working
Each key learning point matches a question type on the printable worksheet.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.