Explanation Given: The matrix is [ 1 3 4 2 0 2 6 − 4 − 1 − 3 − 2 1 ] . 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 3 4 2 0 2 6 − 4 − 1 − 3 − 2 1 ] . 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, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 9.4, Problem 13E

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 12E

Chapter 9.4, Problem 14E

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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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) the entry in the payoff matrix is simultaneously the smallest and largest entries in its row. 2) the optimal strategy for the row player is the maxim

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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.