Consulting Firm: This firm correctly predicts the success of a new game show with an accuracy of 95%. In other words P(Finding of Firm = Successful | New Game Show is Successful) = .95. This firm correctly predicts an unsuccessful new game show with an accuracy of 70%. In other words P(Finding of Firm = Unsuccessful | New Game Show is Unsuccessful) = .7. This firm charges $10,000 for their services. Problem: After hearing about the success of Professor Sharkey as a game show host1, Clemson has decided to consider asking the ACC Network to launch ‘Sharkey’s IE Game Show.’ Based on previous game shows on the network, there is a 60% chance that the game show will be successful and a 40% chance it will be unsuccessful. We will focus on the profits/losses incurred by Clemson through its revenue/cost-sharing agreement with the network. A successful IE-based game show will bring Clemson profits of $125,000 and an unsuccessful IE-based game show will cost Clemson $50,000. Clemson has an opportunity to hire a firm that specializes in reviewing game show concepts2 and predicting their potential success. (a) Construct the decision tree for this problem which includes the decisions of whether or not to hire the firm and whether or not to launch the game show. (b) Find the probabilities for the branches emanating from the chance nodes. Please provide all ‘intermediate probabilities’ (i.e., probabilities you calculated but do not appear in the branches) you used to determine the probabilities relevant to the problem. These probabilities should include P(Finding of Firm = Successful), P(Finding of Firm = Unsuccessful), and all conditional probabilities with respect to the probability of the state of the game show conditioned on the finding of the firm (e.g., one example would be P(State of Game Show = Successful | Finding of Firm = Successful)). (c) Analyze the decision tree to identify the optimal policy. For each chance node, please provide the expected payoff. For each event node, please provide the payoff of that node and the decision that was selected to achieve that payoff. (d) Now suppose that the consulting firm’s fee is negotiable. What is the maximum amount that Clemson should pay them? Please discuss your logic in determining this amount.
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Consulting Firm: This firm correctly predicts the success of a new game show with an accuracy of 95%.
In other words P(Finding of Firm = Successful | New Game Show is Successful) = .95. This firm correctly
predicts an unsuccessful new game show with an accuracy of 70%. In other words P(Finding of Firm =
Unsuccessful | New Game Show is Unsuccessful) = .7. This firm charges $10,000 for their services.
Problem: After hearing about the success of Professor Sharkey as a game show host1, Clemson has decided to consider asking the ACC Network to launch ‘Sharkey’s IE Game Show.’ Based on previous game shows
on the network, there is a 60% chance that the game show will be successful and a 40% chance it will
be unsuccessful. We will focus on the profits/losses incurred by Clemson through its revenue/cost-sharing
agreement with the network. A successful IE-based game show will bring Clemson profits of $125,000 and
an unsuccessful IE-based game show will cost Clemson $50,000. Clemson has an opportunity to hire a firm
that specializes in reviewing game show concepts2 and predicting their potential success.
(a) Construct the decision tree for this problem which includes the decisions of whether or not
to hire the firm and whether or not to launch the game show.
(b) Find the probabilities for the branches emanating from the chance nodes. Please provide
all ‘intermediate probabilities’ (i.e., probabilities you calculated but do not appear in the branches)
you used to determine the probabilities relevant to the problem. These probabilities should include
P(Finding of Firm = Successful), P(Finding of Firm = Unsuccessful), and all conditional probabilities
with respect to the probability of the state of the game show conditioned on the finding of the firm
(e.g., one example would be P(State of Game Show = Successful | Finding of Firm = Successful)).
(c) Analyze the decision tree to identify the optimal policy. For each chance node, please
provide the expected payoff. For each
decision that was selected to achieve that payoff.
(d) Now suppose that the consulting firm’s fee is negotiable. What is the maximum amount that
Clemson should pay them? Please discuss your logic in determining this amount.
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