Minimax- Ch3-3 4. Alice and Bob are playing an adversarial game as shown in the game tree below. Alice (the MAX player) and Bob (the MIN player) are both rational and they both know that their opponent is also a rational player. The game tree has one chance node E whose outcome can be either E=-100 or E = +120with equal 0.5 probability. Alice Bob -20 60 -100 120 Each player's utility is equal to the amount of money he or she has. The value xof each leaf node in the game tree means that Bob will pay Alice xdollars after the game, so that Alice and Bob's utilities will be xand -x respectively. A. Suppose neither Alice nor Bob knows the outcome of E before playing. What is Alice's expected utility? B. Carol, a good friend of Alice's. has access to Eand can secretly tell Alice the outcome of Ebefore

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Minimax- Ch3-3
4. Alice and Bob are playing an adversarial game as shown in the game tree below. Alice (the MAX
player) and Bob (the MIN player) are both rational and they both know that their opponent is also a
rational player. The game tree has one chance node E whose outcome can be either E=- 100 or E
= +120with equal 0.5 probability.
Alice
Bob
-20
E
60
-100
120
Each player's utility is equal to the amount of money he or she has. The value Xof each leaf node in
the game tree means that Bob will pay Alice xdollars after the game, so that Alice and Bob's utilities
will be xand -xrespectively.
A. Suppose neither Alice nor Bob knows the outcome of E before playing. What is Alice's expected
utility?
B. Carol, a good friend of Alice's, has access to Fand can secretly tell Alice the outcome of E'before
the game. However, Bob is not aware of any communication between Alice and Carol, so he still
Transcribed Image Text:Minimax- Ch3-3 4. Alice and Bob are playing an adversarial game as shown in the game tree below. Alice (the MAX player) and Bob (the MIN player) are both rational and they both know that their opponent is also a rational player. The game tree has one chance node E whose outcome can be either E=- 100 or E = +120with equal 0.5 probability. Alice Bob -20 E 60 -100 120 Each player's utility is equal to the amount of money he or she has. The value Xof each leaf node in the game tree means that Bob will pay Alice xdollars after the game, so that Alice and Bob's utilities will be xand -xrespectively. A. Suppose neither Alice nor Bob knows the outcome of E before playing. What is Alice's expected utility? B. Carol, a good friend of Alice's, has access to Fand can secretly tell Alice the outcome of E'before the game. However, Bob is not aware of any communication between Alice and Carol, so he still
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