7.08a-c Zero-sum games, pure strategies and Nash equilibrium Quiz: OCR Further Maths, Unit 4

The 20 questions

1. What is the defining sum of payoffs for all players in a zero-sum game?

   • Positive
   • Zero
   • Constant
   • One

2. Which term describes a strategy where a player chooses one specific option with certainty?

   • Mixed strategy
   • Dominant strategy
   • Pure strategy
   • Play safe strategy

3. What rule determines the play safe strategy for the row player in a payoff matrix?

   • Minimin
   • Maximax
   • Maximin
   • Minimax

4. What rule determines the play safe strategy for the column player in a payoff matrix?

   • Maximax
   • Maximin
   • Minimax
   • Minimin

5. What exists when the maximin value equals the minimax value in a game matrix?

   • Mixed equilibrium
   • Saddle point
   • Fair strategy
   • Dominant row

6. What is the value of a zero-sum game that is defined as fair?

   • Greater than zero
   • Zero
   • Less than zero
   • One

7. In a zero-sum game, what name is given to a saddle point solution?

   • Dominant reduction
   • Mixed strategy
   • Pareto optimal
   • Nash equilibrium

8. How is a row strategy described if all its payoffs are strictly lower than another row's?

   • Strictly dominated
   • Strictly dominant
   • Saddle point
   • Play safe

9. Row minimums for a game are -3, 2, and 1. What is the maximin value?

   • 2
   • 1
   • -3
   • 0

10. Column maximums for a game are 5, 2, and 4. What is the minimax value?

    • 11
    • 2
    • 4
    • 5

11. A zero-sum matrix has maximin value 3 and minimax value 3. What is the game value?

    • 0
    • -3
    • 6
    • 3

12. Row A has payoffs (4, 2) and Row B has payoffs (5, 3). Which row is dominated?

    • Row A
    • Both rows
    • Neither row
    • Row B

13. Column X has payoffs (2, 5) and Column Y has payoffs (1, 4). Which column is dominated?

    • Both columns
    • Neither column
    • Column Y
    • Column X

14. If both players play safe and reach a saddle point, how is the game described?

    • Stable
    • Unfair
    • Unsolvable
    • Mixed

15. Row minimums are 1, -2 and column maximums are 3, 1. Does a saddle point exist?

    • Yes, value 3
    • Yes, value -2
    • Yes, value 1
    • No

16. In a payoff matrix, row entries represent gains for which player in a zero-sum game?

    • Row player
    • Column player
    • Both players
    • Neither player

17. If a zero-sum game matrix has no saddle point, what strategy type must players use?

    • Mixed strategy
    • Pure strategy
    • Play safe strategy
    • Dominant strategy

18. If entry (2, 1) is a saddle point, what happens to Row's payoff if they change row?

    • Becomes zero
    • Doubles
    • Increases
    • Decreases or equals

19. A payoff matrix has two saddle points. What must be true about them?

    • One is strictly greater
    • Payoffs sum to one
    • Both are zero
    • Payoffs are equal

20. At Nash equilibrium, what happens to Column player's loss if they unilaterally change strategy?

    • Becomes negative
    • Increases or equals
    • Drops to zero
    • Decreases

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