Solve the games with the given payoff matrix.
$$P = \left[ \begin{array} { l l l }
- 4 & - 6 & - 3 \
- 4 & - 3 & - 5
\end{array} \right]$$
A) $C = \left[ \begin{array} { c }
0 \
\frac { 10 } { 81 } \
\frac { 5 } { 9 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l }
\frac { 10 } { 81 } & \frac { 5 } { 9 }
\end{array} \right]$ , $e = - \frac { 21 } { 5 }$
B) $C = \left[ \begin{array} { l }
\frac { 2 } { 5 } \
\frac { 3 } { 5 } \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l }
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$ , $e = - \frac { 21 } { 5 }$
C) $C = \left[ \begin{array} { l }
0 \
\frac { 2 } { 5 } \
\frac { 3 } { 5 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l }
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$ , $e = \frac { 21 } { 5 }$
D) $C = \left[ \begin{array} { c }
0 \
\frac { 10 } { 81 } \
\frac { 5 } { 9 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l }
\frac { 10 } { 81 } & \frac { 5 } { 9 }
\end{array} \right]$ , $e = \frac { 21 } { 5 }$
E) $C = \left[ \begin{array} { l }
0 \
\frac { 2 } { 5 } \
\frac { 3 } { 5 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l }
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$ , $e = - \frac { 21 } { 5 }$

Question

Solve the games with the given payoff matrix.  
 $$P = \left[ \begin{array} { l l l } 
- 4 & - 6 & - 3 \
- 4 & - 3 & - 5
\end{array} \right]$$  
A) $C = \left[ \begin{array} { c } 
0 \
\frac { 10 } { 81 } \
\frac { 5 } { 9 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l } 
\frac { 10 } { 81 } & \frac { 5 } { 9 }
\end{array} \right]$ , $e = - \frac { 21 } { 5 }$
B)   $C = \left[ \begin{array} { l } 
\frac { 2 } { 5 } \
\frac { 3 } { 5 } \
0
\end{array} \right]$ , $R = \left[ \begin{array} { l l } 
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$ , $e = - \frac { 21 } { 5 }$
C) $C = \left[ \begin{array} { l } 
0 \
\frac { 2 } { 5 } \
\frac { 3 } { 5 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l } 
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$  , $e = \frac { 21 } { 5 }$
D) $C = \left[ \begin{array} { c } 
0 \
\frac { 10 } { 81 } \
\frac { 5 } { 9 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l } 
\frac { 10 } { 81 } & \frac { 5 } { 9 }
\end{array} \right]$  , $e = \frac { 21 } { 5 }$
E) $C = \left[ \begin{array} { l } 
0 \
\frac { 2 } { 5 } \
\frac { 3 } { 5 }
\end{array} \right]$ , $R = \left[ \begin{array} { l l } 
\frac { 2 } { 5 } & \frac { 3 } { 5 }
\end{array} \right]$ ,  $e = - \frac { 21 } { 5 }$

Quizplus · Accepted Answer

The correct strategy probabilities and the value of the game can be determined by solving the linear programming problem or using the method of solving matrix games. The given payoff matrix does not directly correspond to the strategy probabilities and game value in options A, B, C, or D. Option E correctly identifies the mixed strategy probabilities for the column player (C) and the row player (R), and the value of the game (e) as $-\frac{21}{5}$, which can be derived through calculations specific to the payoff matrix.

Solve the Games with the Given Payoff Matrix P=[−4−6−3−4−3−5]P = \left[ \begin{array} { l l l } - 4 & - 6 & - 3 \\- 4 & - 3 & - 5\end{array} \right]P=[−4−4​−6−3​−3−5​]

Solve the Games with the Given Payoff Matrix $P = \left[ \begin{array} { l l l } - 4 & - 6 & - 3 \\- 4 & - 3 & - 5\end{array} \right]$