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 RokaRola 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 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 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 why it was rational for the decision maker to opt for the alternative having the highest expected utility.