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Question 1 8 Batman and Robin are trying to rescue Catwoman from the Joker. They suspect that the Joker has taken her to one of
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Batman and Robin are trying to rescue Catwoman from the Joker. They suspect that the Joker has taken her to one of his two hideouts: A large cave C or a deserted twostory building B After some deliberation Batman and Robin conclude that the Joker is equally likely to be at either location but if he is in the deserted building, then with probability he will be in his laboratory on the second floor B and with probability of he will be downstairs B Batman and Robin believe that the Joker injected Catwoman with a slow acting poison and wish to rescue her as soon as possible in order to give her the antidote before it is too late.
Batman and Robin have two alternatives:
A Search the building first
A Search the cave first.
The rescue times under each alternative are as follows:
tableIf Joker and Catwoman are inAlternativeBBCA minutes, minutes, minutesA minutes, minutes, minutes
a Find the best strategy for Batman and Robin. What will be the expected rescue time under the optimal strategy?
b A welldressed stranger suddenly appears and offers "partial" perfect information: He only will say whether or not Joker is in the cave. Should Batman and Robin be willing to talk to him for minutes to get his information?
c Suppose the welldressed man offered to provide complete perfect information: He will say exactly where the joker is How long should Batman and Robin be willing to talk to him in that case? Hint: calculate EVPI
dBatman and Robin chose not to talk to the welldressed stranger but instead they consider a test: Robin will go to the deserted building and listen outside for ghoulish laughter. If the Joker is in downstairs then the probability that Robin will hear laughter is If the Joker is in the laboratory upstairs, however, Robin will not hear him laughing with probability Should they make this test before deciding whether to search the cave or the building if it takes minutes in addition to the search times
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