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Figure 10.20.
A simple game tree
T WW L L
L WL
WL
T L T
WW
2.
Consider the game tree depicted in figure 10.20. What is the move that Max
should make from the root node? Answer by labeling every state of the game
tree with
W
,
L
,or
T
(for a tie).
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.