Solve the games with the given payoff matrix. $$\left[ \begin{array} { c c c c }
1 & - 1 & 2 & 0 \
1 & 2 & 0 & 1 \
0 & 1 & 1 & 0 \
2 & 0 & - 2 & 2
\end{array} \right]$$
A) $C = \left[ \begin{array} { c }
\frac { 1 } { 3 } \
\frac { 2 } { 3 } \
0 \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l }
0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$
B) $C = \left[ \begin{array} { c }
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l }
\frac { 1 } { 3 } & \frac { 2 } { 3 } & 0 & 0
\end{array} \right]$ , $e = \frac { 2 } { 3 }$
C) $C = \left[ \begin{array} { c }
\frac { 1 } { 3 } \
\frac { 2 } { 3 } \
0 \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l }
0 & 0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$ , $e = \frac { 2 } { 3 }$
D) $C = \left[ \begin{array} { c }
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l }
0 & 0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$
E) $C = \left[ \begin{array} { c }
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l }
0 & 0 & \frac { 2 } { 3 } & \frac { 1 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$

Question

Solve the games with the given payoff matrix. $$\left[ \begin{array} { c c c c } 
1 & - 1 & 2 & 0 \
1 & 2 & 0 & 1 \
0 & 1 & 1 & 0 \
2 & 0 & - 2 & 2
\end{array} \right]$$  
A) $C = \left[ \begin{array} { c } 
\frac { 1 } { 3 } \
\frac { 2 } { 3 } \
0 \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l } 
0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$
B) $C = \left[ \begin{array} { c } 
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l } 
\frac { 1 } { 3 } & \frac { 2 } { 3 } & 0 & 0
\end{array} \right]$ , $e = \frac { 2 } { 3 }$
C) $C = \left[ \begin{array} { c } 
\frac { 1 } { 3 } \
\frac { 2 } { 3 } \
0 \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l } 
0 & 0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$ , $e = \frac { 2 } { 3 }$
D) $C = \left[ \begin{array} { c } 
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l } 
0 & 0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$  
E) $C = \left[ \begin{array} { c } 
0 \
0 \
\frac { 2 } { 3 } \
\frac { 1 } { 3 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l l l } 
0 & 0 & \frac { 2 } { 3 } & \frac { 1 } { 3 }
\end{array} \right]$ , $e = - \frac { 2 } { 3 }$

Quizplus · Accepted Answer

The correct answer is C because the payoff matrix is a zero-sum game, so the value of the game is zero. The optimal strategies for the row player and the column player are given by the mixed strategies C and R, respectively. The expected payoff for both players is zero.

Solve the Games with the Given Payoff Matrix [1−1201201011020−22]\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]​1102​−1210​201−2​0102​​

Solve the Games with the Given Payoff Matrix $\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]$