(i) Maximin principle
Act |
State of nature |
Minimum pay-off |
S1 |
S2 |
S3 |
S4 |
A1 |
14 |
9 |
10 |
5 |
5 |
A2 |
11 |
10 |
8 |
7 |
7 |
A3 |
9 |
10 |
10 |
11 |
9 |
A4 |
8 |
10 |
11 |
13 |
8 |
Max (5, 7, 9, 8) = 9. Since the maximum pay-off is 9, the optimal decision is A3 according to maximin rule.
(ii) Minimax principle
Act |
State of nature |
Maximum pay-off |
S1 |
S2 |
S3 |
S4 |
A1 |
14 |
9 |
10 |
5 |
14 |
A2 |
11 |
10 |
8 |
7 |
11 |
A3 |
9 |
10 |
10 |
11 |
11 |
A4 |
8 |
10 |
11 |
13 |
13 |
Min (14, 11, 11, 13) = 11. Since the minimum pay-off is 11, the optimal decision A2 and A3 according to minimax rule.