The following is a payoff table. What decision should be made based on the minimax regret criterion?
A)Alternative 1
B)Alternative 2
C)Alternative 3
D)State of Nature C
E)Does not matter

Question

The following is a payoff table.  What decision should be made based on the minimax regret criterion?
A)Alternative 1 
B)Alternative 2 
C)Alternative 3 
D)State of Nature C 
E)Does not matter

Quizplus · Accepted Answer

To apply the minimax regret criterion, we first need to calculate the maximum regret for each alternative under each state of nature.

For Alternative 1: 
- Regret for State of Nature A: 0 
- Regret for State of Nature B: 3 
- Regret for State of Nature C: 4

For Alternative 2: 
- Regret for State of Nature A: 2 
- Regret for State of Nature B: 0 
- Regret for State of Nature C: 5

For Alternative 3: 
- Regret for State of Nature A: 4 
- Regret for State of Nature B: 3 
- Regret for State of Nature C: 0

Next, we need to find the maximum regret for each alternative: 
- Maximum regret for Alternative 1: 4 
- Maximum regret for Alternative 2: 5 
- Maximum regret for Alternative 3: 4

Based on the minimax regret criterion, we want to choose the alternative that minimizes the maximum regret. In this case, Alternative 1 has the lowest maximum regret, so it is the recommended choice.

The Following Is a Payoff Table