3. This question concerns the intuitive understanding of the labels on a game tree.

Suppose players P and Q are playing a game, and each state of the game is labeled with P or Q (as the eventual winner) or neither for a tie.

a. If a state is labeled with P as the winner, which of the following statements are true?

(1) Throughout the game, no matter what either player does, P will eventually win.

(2) Throughout the game, no matter what Q does, P will be able to choose a move that will eventually lead to a win.

(3) Throughout the game, no matter what P does, Q will be unable to choose a move that will eventually lead to a win (for Q).

b. If a state is labeled with neither as winner, which of the following statements are true?

(1) Throughout the game, no matter what either player does, the game will eventually end in a tie.

(2) Throughout the game, no matter what Q does, P will be able to choose a move that will eventually lead to a tie.

(3) Throughout the game, no matter what Q does, P will be able to choose a move that will eventually lead to a tie or a win.

Transcribed Image Text:

Figure 10.21. A numeric game tree 4 7 5 1 9 3 6 9 8 7 2 5 6 3 6 5 2 7 2638 4 0 3 1 8 9 3 7 428