4D.5.3 Reducing pay-off matrices by dominance Quiz: Pearson Edexcel Further Maths, Unit 44

The 20 questions

1. For a row player, when is row A dominated by row B?

   • Every entry A = B
   • Every entry B ≥ A
   • Sum of B < A
   • Every entry A ≥ B

2. Why can a dominated row be safely deleted from a pay-off matrix?

   • Always optimal
   • Zero payoff
   • Always preferred
   • Never played

3. For a column player, when is column J dominated by column K?

   • Every entry K ≤ J
   • Sum of J < K
   • Every entry K ≥ J
   • Every entry J ≤ K

4. How does removing dominated strategies affect the value of a game?

   • It always decreases
   • It remains unchanged
   • It becomes zero
   • It always increases

5. What is the effect of deleting dominated strategies on a game's value?

   • No effect
   • Value increases
   • Value doubles
   • Value decreases

6. How is a pay-off matrix reduced when row 1 is dominated by row 2?

   • Add both rows
   • Delete row 2
   • Delete both rows
   • Delete row 1

7. What is the main benefit of reducing a pay-off matrix before solving?

   • Increases game value
   • Finds saddle points
   • Simplifies the matrix
   • Removes mixed strategies

8. In the matrix [[2, 3, 1], [1, 2, 0]] for the row player, which row is dominated?

   • Column 2
   • Row 2
   • Neither row
   • Row 1

9. For a single row pay-off [2, 3, 1], which column is dominated for the column player by column 1?

   • Column 1
   • Column 2
   • None
   • Column 3

10. After removing column 2 from [[2, 3, 1]], what is the reduced matrix?

    • [2, 1, 3]
    • [2, 1]
    • [2, 3]
    • [1, 3]

11. What is the value of the reduced 1 by 2 game [2, 1]?

    • 1
    • 3
    • 0
    • 2

12. For the matrix E = [[4, 1], [3, 2]], which column is dominated?

    • Neither column
    • Row 1
    • Column 2
    • Column 1

13. After removing the dominated column from E = [[4, 1], [3, 2]], what is the reduced matrix?

    • [[1, 2]]
    • [[2], [1]]
    • [[4], [3]]
    • [[1], [2]]

14. What is the value of the game E = [[4, 1], [3, 2]]?

    • 3
    • 1
    • 4
    • 2

15. In the matrix [[5, 4, 6], [5, 3, 6]], which column is dominated for the column player?

    • Neither column
    • Column 2
    • Column 1
    • Column 3

16. What is the value of the game [[5, 4, 6], [5, 3, 6]]?

    • 6
    • 3
    • 5
    • 4

17. What probability is assigned to a strictly dominated strategy in an optimal mixed strategy?

    • One
    • Zero
    • One half
    • One third

18. For the matrix G = [[1, 2, 3], [0, 1, 2], [2, 3, 4]], what is the value of the game?

    • 3
    • 1
    • 2
    • 4

19. For G = [[1, 2, 3], [0, 1, 2], [2, 3, 4]], which rows are removed by dominance?

    • Row 1 only.
    • Rows 1 and 2.
    • Rows 2 and 3.
    • Row 3 only.

20. What happens to non-dominated optimal strategies when dominated strategies are removed?

    • They turn pure
    • Their probabilities double
    • They become invalid
    • They remain unchanged

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