Consider the following payoff matrix facing two criminals. $$\begin{array} { | l | l | l | }
\hline & { \text { A: Confess } } & \text { A: Not Confess } \
\hline \text { B: Confess } & \text { A: 20yrs, B: 20yrs } & \text { A: 50yrs, B: 2yrs } \
\hline \text { B: Not Confess } & \text { A: 2yrs, B: 50yrs } & \text { A: 10yrs, B: 10yrs } \
\hline
\end{array}$$ Their options are to confess or not to confess. Given this information:
A)A has a dominant strategy but B does not.
B)B has a dominant strategy but A does not.
C)both A and B have dominant strategies.
D)neither A nor B has a dominant strategy.

Question

Consider the following payoff matrix facing two criminals. $$\begin{array} { | l | l | l | } 
\hline & { \text { A: Confess } } & \text { A: Not Confess } \
\hline \text { B: Confess } & \text { A: 20yrs, B: 20yrs } & \text { A: 50yrs, B: 2yrs } \
\hline \text { B: Not Confess } & \text { A: 2yrs, B: 50yrs } & \text { A: 10yrs, B: 10yrs } \
\hline
\end{array}$$ Their options are to confess or not to confess. Given this information:
A)A has a dominant strategy but B does not.
B)B has a dominant strategy but A does not.
C)both A and B have dominant strategies.
D)neither A nor B has a dominant strategy.

Quizplus · Accepted Answer

A dominant strategy is one that is the best choice for a player, no matter what the other player decides to do. In this matrix, confessing is a dominant strategy for both A and B. For A, confessing leads to either 20 years or 2 years, both of which are better than the outcomes if A does not confess (50 years or 10 years). The same logic applies to B.

Consider the Following Payoff Matrix Facing Two Criminals Their Options Are to Confess or Not to Confess