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. The payoffs represent the number of years each will spend in jail. The Nash equilibrium for the payoff matrix shown is:
A)A: 20 years, B: 20 years.
B)A: 50 years, B: 2 years.
C)A: 2 years, B: 50 years.
D)A: 10 years, B: 10 years.

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. The payoffs represent the number of years each will spend in jail. The Nash equilibrium for the payoff matrix shown is:
A)A: 20 years, B: 20 years.
B)A: 50 years, B: 2 years.
C)A: 2 years, B: 50 years.
D)A: 10 years, B: 10 years.

Quizplus · Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, confessing is a dominant strategy for both players because it minimizes their jail time regardless of the other's action. Thus, the Nash equilibrium is when both confess, leading to 20 years each.

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