In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II.
$\left[ \begin{array} { l l }
5 & 2 \
2 & 1
\end{array} \right]$
Which of the following statements is true?
A) The game has no saddlepoint.
B) The game has a saddlepoint; the value of the game is 1.
C) The game has a saddlepoint; the value of the game is 2.
D) The game has a saddlepoint; the value of the game is 5.

Question

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. 
$\left[ \begin{array} { l l } 
5 & 2 \
2 & 1
\end{array} \right]$
 Which of the following statements is true?
A) The game has no saddlepoint.
B) The game has a saddlepoint; the value of the game is 1.
C) The game has a saddlepoint; the value of the game is 2.
D) The game has a saddlepoint; the value of the game is 5.

Quizplus · Accepted Answer

A saddle point in a two-person zero-sum game is a position on the matrix where the minimum element of its row is also the maximum element of its column, or vice versa. In this matrix, the number 2 in the first row and second column is the minimum of the first row and also the maximum of the second column, making it a saddle point. Therefore, the value of the game is 2.

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains [5221]\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right][52​21​]

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains $\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right]$