Calculate the expected value of the game with the given payoff matrix using the mixed strategy supplied.
$P = \left[ \begin{array} { c c c c }
2 & 0 & - 1 & 2 \
- 1 & 0 & 0 & - 2 \
- 2 & 0 & 0 & 1 \
3 & 1 & - 1 & 1
\end{array} \right]$ , $R = [ 1,0,0,0 ]$ , $C = [ 1,0,0,0 ] ^ { T }$
A) $e = 2$
B) $e = 1.5$
C) $e = 3.5$
D) $e = 3$
E) $e = 4$

Question

Calculate the expected value of the game with the given payoff matrix using the mixed strategy supplied.   
$P = \left[ \begin{array} { c c c c } 
2 & 0 & - 1 & 2 \
- 1 & 0 & 0 & - 2 \
- 2 & 0 & 0 & 1 \
3 & 1 & - 1 & 1
\end{array} \right]$ , $R = [ 1,0,0,0 ]$ , $C = [ 1,0,0,0 ] ^ { T }$  
A) $e = 2$
B)   $e = 1.5$
C)   $e = 3.5$
D)   $e = 3$
E)   $e = 4$

Quizplus · Accepted Answer

The expected value $e$ of the game is calculated using the payoff matrix $P$, row strategy vector $R$, and column strategy vector $C$. Since $R = [1,0,0,0]$ and $C = [1,0,0,0]^T$, it means both the row player and the column player choose their first strategies with probability 1. The expected value is the element in the first row and first column of $P$, which is $2$.

Calculate the Expected Value of the Game with the Given P=[20−12−100−2−200131−11]P = \left[ \begin{array} { c c c c } 2 & 0 & - 1 & 2 \\- 1 & 0 & 0 & - 2 \\- 2 & 0 & 0 & 1 \\3 & 1 & - 1 & 1\end{array} \right]P=​2−1−23​0001​−100−1​2−211​​

Calculate the Expected Value of the Game with the Given $P = \left[ \begin{array} { c c c c } 2 & 0 & - 1 & 2 \\- 1 & 0 & 0 & - 2 \\- 2 & 0 & 0 & 1 \\3 & 1 & - 1 & 1\end{array} \right]$