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Question 1
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem without probabilities.
State of Nature
Alternatives
S1
S2
S3
S4
A1
25
30
20
24
A2
17
14
31
21
A3
22
A4
29
26
27
Question 2
Warren Buffy is an enormously wealthy investor who has built his future through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one. The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in worsening economy. The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a countercyclical investment that would loss some money in an improving economy but would perform well in a worsening economy.
Warren believes that there are three possible scenarios over the lives of these potential investment: (1) an improving economy, (2) a stable economy and (3) a worsening economy. He is pessimistic about where the economy is headed, and so has assigned prior possibilities of 0.1, 0.5, and 0.4 respectively to these three scenarios. He also estimates that his profits under these respective scenarios are those given by the following table.
Improving
Economy ( $)
Stable
Economy ($)
Worsening Economy ($)
Conservative
Investment
30 million
5million
-10million
Speculative
40million
10million
-30million
Countercyclical
0
15million
Prior probability
0.1
0.5
0.4
Which investment should Warren make under each of the following criteria?
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