3. Dominance and Rationalizability

Best Responses — Quiz

Test your understanding of best responses with 5 practice questions.

Practice Questions

Question 1

The payoff matrix lists payoffs as $(\text{row},\text{column})$: $$\begin{array}{c|cc} & L & R \\ \hline U & (4,1) & (0,2) \\ D & (1,3) & (2,0) \end{array}$$. If Column chooses $L$, what is Row's best response?

Question 2

The payoff matrix lists payoffs as $(\text{row},\text{column})$: $$\begin{array}{c|cc} & L & R \\ \hline U & (2,5) & (3,1) \\ D & (0,4) & (1,2) \end{array}$$. If Row chooses $U$, what is Column's best response?

Question 3

The payoff matrix lists payoffs as $(\text{row},\text{column})$: $$\begin{array}{c|cc} & L & R \\ \hline A & (6,0) & (0,4) \\ B & (2,1) & (2,3) \end{array}$$. If Column plays $L$ with probability $\frac{1}{2}$ and $R$ with probability $\frac{1}{2}$, what is Row's best response?

Question 4

The payoff matrix lists payoffs as $(\text{row},\text{column})$: $$\begin{array}{c|cc} & L & R \\ \hline U & (1,6) & (4,1) \\ D & (3,2) & (0,5) \end{array}$$. If Row plays $U$ with probability $\frac{3}{4}$ and $D$ with probability $\frac{1}{4}$, what is Column's best response?

Question 5

The payoff matrix lists payoffs as $(\text{row},\text{column})$: $$\begin{array}{c|ccc} & X & Y & Z \\ \hline A & (2,1) & (1,0) & (3,2) \\ B & (4,3) & (0,2) & (1,1) \\ C & (1,4) & (5,0) & (2,3) \end{array}$$. If Column chooses $Y$, what is Row's best response?