Explanation Given: The matrix is [ − 1 2 4 2 3 5 0 1 − 3 − 2 4 − 2 ] . Approach: To determine the game is strictly determined. A strictly determined game is characterized by the following properties: 1) There is an entry in the payoff matrix that is simultaneously the smallest entry in its row and the largest entry in its column. This entry is called the saddle point for the game. 2) The optimal strategy for the row player is the maximin strategy. obtained by choosing the row containing the saddle point. The optimal strategy for the column player is the minimax strategy. obtained by choosing the column containing the saddle point. Calculation: The given matrix is [ − 1 2 4 2 3 5 0 1 − 3 − 2 4 − 2 ] . First determine the minimum of each row and the maximum of each column of the payoff matrix A and display these minima and maxima as follows To determine b) To find: The optimal strategy for each player. To determine c) To find: The value of the game. To determine d) Whether the game favors row or column player.

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

11th Edition

ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

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Chapter 9.4, Problem 16E

To determine

a)

Whether the game is strictly determined and find the saddle point(s) of the game.

To determine

b)

To find:

The optimal strategy for each player.

To determine

c)

To find:

The value of the game.

To determine

d)

Whether the game favors row or column player.

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Chapter 9.4, Problem 15E

Chapter 9.4, Problem 17E

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Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

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a) Whether the game is strictly determined and find the saddle point(s) of the game.

Solution Summary: The author explains that a strictly determined game is characterized by the following properties: 1) there is an entry in the payoff matrix that is simultaneously the smallest entry and the largest entry. 2) The optimal strategy for the row player is

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a) Whether the game is strictly determined and find the saddle point(s) of the game.

b) To find: The optimal strategy for each player.

c) To find: The value of the game.

d) Whether the game favors row or column player.

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Chapter 9 Solutions

a)

Whether the game is strictly determined and find the saddle point(s) of the game.

b)

To find:

The optimal strategy for each player.

c)

To find:

The value of the game.

d)

Whether the game favors row or column player.