The Roka-Rola drinks company is engaged in continuous competition

for market share with its rival Tepsi. Recent technological

developments have led to the possibility of Roka-Rola including

a device in its cans which instantly cools the drink when the can

is opened. However, incorporating the device would be expensive

and the company must decide now whether or not to go ahead

with the development. Because of other competing demands on the

company's capital, a decision not to go ahead now could not be

easily reversed.

If Roka-Rola does not incorporate the device then there is thought

to be only a 0.4 probability that Tepsi will include it in its cans.

If Tepsi does include it in an attempt to steal a march on Roka-

Rola then Roka-Rola would consider defending its position by

making some changes to the ingredients in the drink in an attempt

to improve its flavor, though this would be a risky strategy. A

decision not to change the ingredients would mean that there was

a 0.8 probability that Roka-Rola's market share would fall to only

10% within a year and a 0.2 probability that it would fall to 20%.

A decision to change the ingredients would lead to a 0.3 risk of

only a 5% market share being achieved, but a 0.7 probability that

the market share would reach 30% in a year's time. Changing the

ingredients would only be considered if Tepsi included the device

in its cans. If Tepsi, like Roka-Rola, did not incorporate the device

then it is thought to be virtually certain that Roka-Rola's existing

market share of 25% will be maintained.

If a decision was made by Roka-Rola to incorporate the device

in its cans then there is thought to be a 0.7 probability that Tepsi

would retaliate and include a device in its own cans. If they did

not, then there would be a 0.2 probability of Roka-Rola achieving

a 40% market share by the end of the year and a 0.8 probability

that it would achieve a 50% market share. If Tepsi did retaliate then

Roka-Rola would have to consider changing the ingredients of the

product. A decision to change the ingredients would, it is thought,

be certain to leave Roka-Rola's market share unchanged at 25%.

However, changing the ingredients would lead to a 0.7 probability

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. Determinehowsensitive 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

are to be used to make the decision.

(iii) Interpret the expected utilities you obtained for the options

of including and not including the device and explain

Exercises 173

why it was rational for the decision maker to opt for the

alternative having the highest expected utility.