Explanation Given: The matrix is [ 3 − 1 0 − 4 2 1 0 2 − 3 1 − 2 1 − 1 − 1 − 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 [ 3 − 1 0 − 4 2 1 0 2 − 3 1 − 2 1 − 1 − 1 − 2 1 ] 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 18E

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 17E

Chapter 9.4, Problem 19E

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Chapter 9 Solutions

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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 the game is strictly determined and the entry a_23=0 is its saddle point. The optimal strategy for the row player is the maximin strategy.

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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.