The following is a payoff table giving costs for various situations. What decision should be made based on the minimax regret criterion?
A)Alternative 1
B)Alternative 2
C)Alternative 3
D)Alternative 4

Question

The following is a payoff table giving costs for various situations.  What decision should be made based on the minimax regret criterion?
A)Alternative 1 
B)Alternative 2 
C)Alternative 3 
D)Alternative 4

Quizplus · Accepted Answer

To use the minimax regret criterion, we first need to calculate the regrets for each cell by subtracting the minimum payoff in the same column from each of the payoffs in that cell. Then, we find the maximum regret for each alternative and select the alternative with the minimum maximum regret. The regret table is as follows:

|           | Alternative 1 | Alternative 2 | Alternative 3 | Alternative 4 |
|-----------|---------------|---------------|---------------|---------------|
| Outcome 1 | 0             | 10            | 10            | 20            |
| Outcome 2 | 2             | 0             | 8             | 16            |
| Outcome 3 | 6             | 6             | 0             | 12            |
| Outcome 4 | 10            | 8             | 2             | 0             |

The maximum regret for Alternative 1 is 10 (the regret for Outcome 2), for Alternative 2 it is 8 (the regret for Outcome 4), for Alternative 3 it is 10 (the regret for Outcome 1), and for Alternative 4 it is 20 (the regret for Outcome 1). Therefore, the best choice is Alternative 2, as it has the minimum maximum regret of 8.

The Following Is a Payoff Table Giving Costs for Various