Dominance and mixed strategies Quiz

1. Row 1 is $(2,\ 3,\ 1)$ and row 2 is $(4,\ 3,\ 2)$. Which statement is true?

• A. Row 1 dominates row 2
• B. Row 2 dominates row 1
• C. Neither dominates
• D. Row 1 is dominated only in column 2

2. Column 1 is $(3,\ 2)$ and column 2 is $(5,\ 4)$. Which column does Colin never play?

• A. Column 1
• B. Neither
• C. Column 2
• D. Both

3. Rowan plays row 1 with probability $p$. His pay-offs against Colin's two columns are $3p+2$ and $4-3p$. What is the optimal $p$?

• A. $\frac13$
• B. $\frac12$
• C. $\frac23$
• D. $\frac14$

4. In the graphical method for Rowan, which point is chosen?

• A. The lowest point of the upper boundary
• B. The highest point of the lower boundary
• C. The intersection of the two steepest lines
• D. The point where $p=\frac12$

5. At the optimal $p$, a third line lies above the intersection of the other two. What does this show?

• A. Rowan should never play row 1
• B. The game is stable
• C. The value is the third line's height
• D. Colin never plays that column