Topic summary · Student revision
Game Theory Topic Review summary
Self-review on zero-sum games, play-safe strategies, and mixed-strategy equilibria for games.
Files: Topic-Review-Game-Theory.pdf · Topic-Review-Game-Theory-Answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Pay-off matrix from the row player’s viewpoint (usually).
- Play-safe: maximin for rows, minimax for columns.
- Saddle point: entry that is both maximin and minimax — stable pure strategy.
- No saddle ⇒ mixed strategies; solve for probabilities making opponent indifferent.
- Value of the game is the expected pay-off under optimal mixed strategies.
Worked example 1 — Saddle
What is a saddle point?
Working
Stable pure-strategy solution.
Worked example 2 — Mixed
Idea of mixed strategy in 2×2.
Working
Then solve for p.
Worked example 3 — Practice point 1
Apply this idea from the Topic Review: Pay-off matrix from the row player’s viewpoint (usually).
Working
Attempt without notes, then check the answers PDF.
Worked example 4 — Practice point 2
Apply this idea from the Topic Review: Play-safe: maximin for rows, minimax for columns.
Working
Attempt without notes, then check the answers PDF.
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.