In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $$\left[ \begin{array} { l l l l }
8 & 1 & 5 & 2 \
5 & 4 & 7 & 8 \
1 & 3 & 4 & 5 \
8 & 4 & 3 & 5
\end{array} \right]$$ 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 2.
C) The game has a saddlepoint; the value of the game is 3.
D) The game has a saddlepoint; the value of the game is 4.

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. $$\left[ \begin{array} { l l l l } 
8 & 1 & 5 & 2 \
5 & 4 & 7 & 8 \
1 & 3 & 4 & 5 \
8 & 4 & 3 & 5
\end{array} \right]$$ 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 2.
C) The game has a saddlepoint; the value of the game is 3.
D) The game has a saddlepoint; the value of the game is 4.

Quizplus · Accepted Answer

The saddlepoint is the largest of the row minimums and the smallest of the column maximums, which is 4.

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains [8152547813458435]\left[ \begin{array} { l l l l } 8 & 1 & 5 & 2 \\5 & 4 & 7 & 8 \\1 & 3 & 4 & 5 \\8 & 4 & 3 & 5\end{array} \right]​8518​1434​5743​2855​​

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains $\left[ \begin{array} { l l l l } 8 & 1 & 5 & 2 \\5 & 4 & 7 & 8 \\1 & 3 & 4 & 5 \\8 & 4 & 3 & 5\end{array} \right]$