In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.
$\left[ \begin{array} { c c }
1 & - 4 \
- 2 & - 6
\end{array} \right]$
Which of the following statements is true?
A) The game has no saddlepoint.
B) There is a saddlepoint at row 2, column 2.
C) There is a saddlepoint at row 2, column 1.
D) There is a saddlepoint at row 1, column 2.

Question

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. 
$\left[ \begin{array} { c c } 
1 & - 4 \
- 2 & - 6
\end{array} \right]$ 
Which of the following statements is true?
A) The game has no saddlepoint.
B) There is a saddlepoint at row 2, column 2.
C) There is a saddlepoint at row 2, column 1.
D) There is a saddlepoint at row 1, column 2.

Quizplus · Accepted Answer

To check for a saddle point, we need to find the minimum of the maximum values for each row and the maximum of the minimum values for each column. 
- For Row 1: the maximum value is 1. 
- For Row 2: the maximum value is -2. 
- For Column 1: the minimum value is -2. 
- For Column 2: the minimum value is -6. 
The maximum of the minimum values for each column is -2, which is attained at row 1, column 2. This is the saddle point. Therefore, the answer is D.

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains [1−4−2−6]\left[ \begin{array} { c c } 1 & - 4 \\- 2 & - 6\end{array} \right][1−2​−4−6​]

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains $\left[ \begin{array} { c c } 1 & - 4 \\- 2 & - 6\end{array} \right]$