Lesson DF1-DF4

DF1-DF4 Pay-off matrices, play-safe strategies and dominance Quiz: AQA Further Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson DF1-DF4, Pay-off matrices, play-safe strategies and dominance: 20 multiple choice questions for the AQA Further Maths (7367), Unit 5: Optional application 3: discrete mathematics, written with Revision Ninja.

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The 20 questions

  1. What does a pay-off matrix record in a zero-sum game?

    • Combined game profits
    • Column player gains
    • Row player gains
    • Total player losses

  2. In a zero-sum game, what is the sum of all players' pay-offs?

    • Zero
    • One
    • Maximum row value
    • Matrix dimension

  3. Which value does a play-safe strategy for the row player maximise?

    • Minimum column payoff
    • Average row payoff
    • Minimum row payoff
    • Maximum row payoff

  4. What does the value of a zero-sum game represent with optimal play?

    • Guaranteed row payoff
    • Saddle point sum
    • Maximum column loss
    • Zero net utility

  5. A zero-sum game has pay-off matrix (gains to the row player A) with rows A1: 2 4 1; A2: 3 5 4; A3: 1 3 0, and columns B1, B2, B3. What is the value of this game?

    • 4
    • 2
    • 5
    • 3

  6. What is the saddle point value for a game with matrix rows A1(2,4,1), A2(3,5,4), A3(1,3,0)?

    • 4
    • 1
    • 5
    • 3

  7. For matrix rows A1(2,4,1), A2(3,5,4), A3(1,3,0), which is the play-safe row?

    • Row A1
    • Row B1
    • Row A3
    • Row A2

  8. A zero-sum game has pay-off matrix (gains to the row player A) with rows A1: 3 -1; A2: -2 4, and columns B1, B2. What is the play-safe value for the row player, using the maximin method?

    • 4
    • 1
    • 3
    • -1

  9. Does a zero-sum game with rows A1(3,-1) and A2(-2,4) have a stable solution in pure strategies?

    • Undefined
    • Yes
    • No
    • Infinitely many

  10. A zero-sum game has pay-off matrix (gains to the row player A) with rows A1: 3 -1; A2: -2 4, and columns B1, B2. In an optimal mixed strategy, what probability does the row player assign to A1?

    • 0.4
    • 0.6
    • 0.3
    • 0.5

  11. A zero-sum game has pay-off matrix (gains to the row player A) with rows A1: 3 -1; A2: -2 4, and columns B1, B2. What is the value of this game when both players use optimal mixed strategies?

    • 2
    • 0
    • -1
    • 1

  12. For matrix rows A1(2,3,1) and A2(1,2,0), which row dominates the other?

    • A1 dominates A2
    • Both rows dominate
    • A2 dominates A1
    • Neither row dominates

  13. For row A1(2,3,1) with columns B1, B2, B3, which column should player B choose?

    • Column B2
    • Column B1
    • Row A1
    • Column B3

  14. What properties must the value of a saddle point satisfy in a pay-off matrix?

    • Row min, column min
    • Row max, column min
    • Row max, column max
    • Row min, column max

  15. What can be done with a dominated row in a pay-off matrix?

    • It must be doubled
    • It becomes the value
    • It defines pure strategy
    • It can be deleted

  16. For matrix rows A1(2,4,1), A2(3,5,4), A3(1,3,0), which rows are dominated?

    • A1 only
    • A3 only
    • A1 and A3
    • A2 only

  17. For any pay-off matrix in a two-person zero-sum game, which inequality always holds between the maximin and minimax values?

    • Maximin ≥ minimax
    • Maximin + minimax = 0
    • Maximin = minimax always
    • Maximin ≤ minimax

  18. If only row A2(3,5,4) remains, which column B1, B2, or B3 will player B choose?

    • Column B1
    • Row A2
    • Column B2
    • Column B3

  19. In a zero-sum game with a saddle point, how do maximin and minimax relate?

    • Minimax is larger
    • They are equal
    • They are unrelated
    • Maximin is larger

  20. When should a player use a mixed strategy in a zero-sum game?

    • Saddle point exists
    • Positive payoffs only
    • No saddle point
    • Strictly dominant row

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