In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Which of the following statements is true?
A) The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the first column.
B) The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the first column.
C) The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the second column.
D) The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the second column.

Question

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.  Which of the following statements is true?
A) The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the first column. 
B) The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the first column. 
C) The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the second column. 
D) The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the second column.

Quizplus · Accepted Answer

To find the maximin strategy of player I, we find the minimum payoffs for each of their possible moves:

- Playing the first row: minimum payoff is -4
- Playing the second row: minimum payoff is -3

Player I will choose the row that maximizes their minimum payoff, so they will play the second row.

To find the minimax strategy of player II, we find the maximum payoffs for each of their possible moves:

- Playing the first column: maximum payoff is 3
- Playing the second column: maximum payoff is 2

Player II will choose the column that minimizes their maximum payoff, so they will play the second column.

Therefore, the maximin strategy of player I is to always play the second row, and the minimax strategy of player II is to always play the second column. So, the correct answer is D.

In the Following Two-Person Zero-Sum Game, the Payoffs Represent Gains