Which alternative should be chosen under the maxi-max

Question

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	22	22	22
A4	29	21	26	27

1. which alternative should be chosen under the maxi-max criterion?
2. Which alternative should be chosen under the maxi-min criterion?

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 Investment	40million	10million	-30million
Countercyclical Investment	-10million	0	15million
Prior probability	0.1	0.5	0.4

Which investment should Warren make under each of the following criteria?

1. maxi-max criterion
2. maxi-min criterion
3. maximum likelihood criterion

1. set up the spreadsheetand use solver for: Bayes' decision rule