Assignment Choice under Uncertainty

Task

We have four alternatives A1, A2, A3, and A4 to choose from. There are also four situations S1, S2, S3, and S4 that cause different pay-offs for each alternative. Furthermore, the probability of occurrence of those four situations is unknown.

	S1	S2	S3	S4
A1	10	10	5	8
A2	9	10	12	8
A3	15	3	2	-2
A4	14	4	3	0

What alternative should you select under the following decision rules:

• LaPlace rule?
• Maxmin-rule
• Maximax rule
• Range rule (lowest rank = 1)
• Minimax regret rule
• Hurzwicz rule (optimism parameter a = 0.3)

Solution

	S1	S2	S3	S4	LaPlace	Maximin Rule	Maximax rule	Range rule	Minimax Regrett	Hurwicz
A1	10	10	5	8	8.25	5	10	7	7	6.5
A2	9	10	12	8	9.75	8	12	7	6	9.2
A3	15	3	2	-2	4.5	-2	15	11	10	3.1
A4	14	4	3	0	5.25	0	14	9	8	4.2

The bold numbers show the choice for each rule.