Decision Minimax/min
Posted on July 1, 2015
Tags: Economics
| Present Choice | Best future | Typical future | Worst future |
|---|---|---|---|
| invest 8 | +8 | +2 | -4 |
| invest 4 | +4 | +1 | -2 |
| invest 2 | +2 | +0.5 | -1 |
| invest 1 | +1 | +0.25 | -0.5 |
| No action | 0 | 0 | 0 |
1 Maximin
\[Decision = Min(Worst_Future)\] \[Decision = Min({-4,-2,-3,-0.5,0\}) = 0\] \[Decision = No\ Action\]
2 Maximax
Choose the decision Max of Best future col which is +8 corresponding to “invest 8”
\[Decision = Min(Best_Future)\] \[Decision = Min({+8,+4,+2,+1,0\}) = 0\] \[Decision = invest\ 8\]
3 Regret
| Present Choice | Best future | Typical future | Worst future |
|---|---|---|---|
| invest 8 | +8 -8 | +2 -2 | -4 -0.5 |
| invest 4 | +4 -8 | +1 -2 | -2 -0.5 |
| invest 2 | +2 -8 | +0.5 -2 | -1 -0.5 |
| invest 1 | +1 -8 | +0.25 -2 | -0.5 -0.5 |
| No action | 0 -8 | 0 -2 | 0 -0.5 |
- Regret for a single column = Current returns - Max returns
- This means the best decision in a chosen future should have 0 regret.
4 Expected value
Each future has a probability. So we calculate expected value for each investment choice.
