Game theory foundations

Security before mixing

For a zero-sum payoff matrix, the row player protects against the worst payoff in each row and chooses the largest row minimum: the maximin. The column player chooses the smallest column maximum: the minimax.

If maximin equals minimax at a cell, that cell is a saddle point and pure strategies suffice. Without a saddle point, a 2×2 interior game may require mixed strategies that make the opponent indifferent.