Finite Mathematics : Games and Decisions

Study concepts, example questions & explanations for Finite Mathematics

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Example Questions

Example Question #1 : Games And Decisions

Consider the following payoff matrix for a game:

Give the value of the saddle point entry of the matrix, if it exists.

Possible Answers:

The matrix has no saddle point.

Correct answer:

Explanation:

If a payoff matrix has a saddle point, it must be both the minimum element of its row and the maximum element of its column. The minimum element of each row is shown in red:

 

Of these three entries, only 75 is the maximum of its column. This is the correct choice.

Example Question #2 : Games And Decisions

Consider the following payoff matrix for a game:

Give the value of the saddle point entry of the matrix, if it exists.

Possible Answers:

The matrix has no saddle point.

Correct answer:

Explanation:

If a payoff matrix has a saddle point, it must be both the minimum element of its row and the maximum element of its column. The minmum element of each row is shown in red:

Both saddle point entries are in Column 3, so we select the greater of the two, , as the saddle point entry.

Example Question #3 : Games And Decisions

Consider the following payoff matrix for a game:

Give the value of the saddle point entry of the matrix, if it exists.

Possible Answers:

The matrix has no saddle point.

Correct answer:

Explanation:

If a payoff matrix has a saddle point, it must be both the minimum element of its row and the maximum element of its column. The minimum element of each row is shown in red:

Of the three, only 100 is the maximum element of its column. This is the saddle point entry.

Example Question #4 : Games And Decisions

Consider the following payoff matrix for a game:

Give the value of the saddle point entry of the matrix, if it exists.

Possible Answers:

The matrix has no saddle point.

Correct answer:

Explanation:

If a payoff matrix has a saddle point, it must be both the minimum element of its row and the maximum element of its column. The minimum element of each row is shown in red:

Of the three, only 500 is the maximum of its column, making 500 the saddle point entry.

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