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.

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ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

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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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Determine whether the two-person, zero-sum matrix game is strictly determined. 2 0 -5 Yes, it is strictly determined. O No, it is not strictly determined. If the game is strictly determined, answer the following. (If the game is not strictly determined, enter DNE for each.) (a) Find the saddle point of the game. (b) Find the optimal strategy for each player. The optimal strategy for the row player is to play row The optimal strategy for the column player is to play column (c) Find the value of the game. (d) Determine whether the game favors one player over the other. O It favors the row player. O It favors the column player. O It is fair. O It is not strictly determined. (DNE)

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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.