Question

Using the MINIMAX regret method, which decision alternative will you chose?
a) Sell company

b) Form Joint Venture

c) Sell software on own
Success Moderate Success Failure
Sell Company 100 245 400
Form Joint Venture 250 -200 -100
Sell Software on own 220 120 200

Answer 1

To utilize the MINIMAX regret method, we first need to find the maximum payoff for each state of nature (Success, Moderate Success, Failure). Next, we'll calculate the regret for each decision alternative, find the maximum regret for each alternative, and then choose the alternative with the minimum of these maximum regrets.

### Step 1: Identify Maximum Payoffs for Each State

- **Success**: The maximum payoff is **250** (from the "Form Joint Venture" alternative).
- **Moderate Success**: The maximum payoff is **245** (from the "Sell Company" alternative).
- **Failure**: The maximum payoff is **400** (also from the "Sell Company" alternative).

### Step 2: Calculate Regrets

Now we'll calculate regret for each decision alternative by subtracting each alternative's payoff from the maximum payoff for each state.

#### Regret Table:

| Decision Alternative | Success Regret | Moderate Success Regret | Failure Regret |
|---------------------------|----------------|-------------------------|-----------------|
| Sell Company | 250 - 100 = 150| 245 - 245 = 0 | 400 - 400 = 0 |
| Form Joint Venture | 250 - 250 = 0 | 245 - (-200) = 445 | 400 - (-100) = 500 |
| Sell Software on own | 250 - 220 = 30 | 245 - 120 = 125 | 400 - 200 = 200 |

### Step 3: Maximum Regret for Each Alternative

Now we find the maximum regret for each alternative:

- **Sell Company**: Max(150, 0, 0) = 150
- **Form Joint Venture**: Max(0, 445, 500) = 500
- **Sell Software on own**: Max(30, 125, 200) = 200

### Step 4: Choose Minimum of Maximum Regrets

Finally, we compare the maximum regrets:

- Sell Company: 150
- Form Joint Venture: 500
- Sell Software on own: 200

The alternative with the **minimum maximum regret** is "Sell Company" with a maximum regret of **150**.

### Conclusion

Using the MINIMAX regret method, you should **choose to Sell the Company**.