Downloadable - About University

172 Decision trees and influence diagrams
that Roka-Rola’s market share would fall to 15% by the end of the
year and a 0.3 probability that it would rise to 45%.
(a) Assuming that Roka-Rola’s objective is to maximize the expected
market share which will be achieved in a year’s time, determine
the company’s optimal policy.
(b) There is some doubt about the 0.4 probability which was estimated
for Tepsi including the device in its cans when Roka-Rola
had rejected the idea. Determine how sensitive Roka-Rola’s decision
on whether to include the device is to this probability and
explain your answer.
(c) Utilities for market share have been elicited from Roka-Rola’s
marketing manager. These are given below (note that two values
have been omitted):
Market share Utility
5% 0
10% 0.25
15% 0.45
20% omitted
25% 0.72
30% omitted
40% 0.95
45% 0.98
50% 1.00
During the elicitation process it was established that the marketing
manager would be indifferent between achieving a market
share of 20% for certain and taking a gamble that would lead to
market shares of either 50% or 5%, with probabilities of 0.6 and
0.4, respectively.
He would also be indifferent between achieving a 30% market
share for certain or entering a gamble which would have a 0.8
probability of yielding a 50% market share and a 0.2 probability
of a 5% market share.
(i) Determine the marketing manager’s attitude to risk and
explain how you were able to determine it.
(ii) Determine whether the optimal policy you identified in part
(a) should be revised if the marketing manager’s utilities
aretobeusedtomakethedecision.
(iii) Interpret the expected utilities you obtained for the options
of including and not including the device and explain