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CSC 5350 Assignment 3
Due date: 7 December 2009
1.
Amy, Betty and Cindy play the following game using one red box and
one yellow box on the table.
First, Amy puts a coin in either the red box or the yellow box.
Betty
and Cindy are not allowed to see which box Amy puts the coin in,
so they do not know whether the coin is in the red box or the yellow
box.
Then, either Betty or Cindy should guess where the coin is, and who
should guess is decided randomly.
The probability that Betty
should guess is
B
p
, and that Cindy should guess is
C
p
, where
1
BC
pp
.
If Betty should guess, and she guesses correctly, then both Amy and
Betty win, and Cindy loses the game.
However, if Betty should
guess, but she guesses incorrectly, then both Amy and Betty lose,
and Cindy wins the game.
Similarly, if Cindy should guess, and she guesses correctly, then
both Amy and Cindy win, but Betty loses the game.
However, if
Cindy should guess, but she guesses incorrectly, then both Amy and
Cindy lose, and Betty wins the game.
For all players, the utility of winning is 1, and the utility of losing is 0.
(a)
Model the game as an extensive game with imperfect information
,
, , ,( ),(
)
c
i
i
G
N H P f
.
i.
Write down
N
in the game
G
.
ii.
Write down
H
in the game
G
.
iii.
Write down
P
in the game
G
.
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 Winter '09
 LeungHoFung
 Computer Science

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