Question

Sell Company 200 535 223

Form Joint Venture 300 334 -100
Sell Software on own 600 333 -120

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

b) Form Joint Venture

c) Sell software on own

Answer 1

To apply the MINIMAX regret method, we first need to calculate the regret for each decision under each state of nature. Regret represents the opportunity loss for not choosing the best decision given a specific state of nature.

Let's outline the payoffs for each alternative you provided:

1. **Sell Company:** 200, 535, 223
2. **Form Joint Venture:** 300, 334, -100
3. **Sell Software on Own:** 600, 333, -120

### Step 1: Identify the Best Payoff for Each State

- **State 1:** Sell Software on Own (600)
- **State 2:** Sell Company (535)
- **State 3:** Sell Company (223)

### Step 2: Calculate Regrets

Now we compute the regret for each decision option in each scenario by subtracting the payoff of the specific option from the best payoff for that state.

#### Regrets for Selling Company
- State 1: 600 - 200 = 400
- State 2: 535 - 535 = 0
- State 3: 223 - 223 = 0
- **Total Regret for Sell Company:** 400, 0, 0

#### Regrets for Forming Joint Venture
- State 1: 600 - 300 = 300
- State 2: 535 - 334 = 201
- State 3: 223 - (-100) = 323
- **Total Regret for Form Joint Venture:** 300, 201, 323

#### Regrets for Selling Software on Own
- State 1: 600 - 600 = 0
- State 2: 535 - 333 = 202
- State 3: 223 - (-120) = 343
- **Total Regret for Sell Software on Own:** 0, 202, 343

### Step 3: Maximum Regret for Each Alternative
Now we find the maximum regret for each decision alternative from the calculated regrets:

- **Sell Company:** 400
- **Form Joint Venture:** 323
- **Sell Software on Own:** 343

### Step 4: MINIMAX Regret
The aim of the MINIMAX regret strategy is to minimize the maximum regret. Thus, we choose the alternative with the lowest maximum regret:

- Sell Company: 400
- Form Joint Venture: 323
- Sell Software on Own: 343

### Conclusion:
The decision alternative that minimizes maximum regret is:

**b) Form Joint Venture** with a maximum regret of 323.