How to find profit to put into payoff table in decision analysis under risk?

To find the profit to put into a payoff table in decision analysis under risk, you will need to consider the potential outcomes and associated probabilities for each decision or strategy.

1. Identify the possible outcomes: Start by listing all the possible outcomes or scenarios that could result from each decision or strategy. For example, if you are considering launching a new product, the outcomes could include high sales, moderate sales, low sales, or no sales.

2. Assign probabilities: Determine the likelihood or probability of each outcome occurring. This could be based on historical data, market research, expert opinions, or other sources of information. For example, you may estimate that there is a 30% chance of high sales, a 40% chance of moderate sales, a 20% chance of low sales, and a 10% chance of no sales.

3. Calculate the profit for each outcome: For each outcome, calculate the profit or financial impact that it would have on your business. This could include revenue, costs, and any other relevant factors. For example, if high sales result in a profit of $100,000, moderate sales result in a profit of $50,000, low sales result in a profit of $10,000, and no sales result in a loss of $20,000, these would be the profits associated with each outcome.

4. Calculate the expected profit: Multiply the probability of each outcome by the profit associated with that outcome, and then sum these values to calculate the expected profit for each decision or strategy. This will give you a clearer picture of the potential financial impact of each option.

5. Populate the payoff table: Once you have calculated the expected profit for each decision or strategy, populate the payoff table with these values. This will allow you to compare the potential outcomes and make an informed decision based on the expected financial impact of each option.

Calculating Profit for Payoff Table in Decision Analysis under Risk

Step 1: Determine the Probability of Each State of Nature

- Identify the possible states of nature that could impact the outcome of the decision.
- Assign probabilities to each state of nature based on available information or expert judgment.

Step 2: Calculate the Expected Value of Each Action in Each State of Nature

- For each action and state of nature combination, calculate the profit or loss that would be incurred.
- Multiply this profit/loss by the probability of the state of nature occurring.

Step 3: Find the Expected Profit for Each Action

- Sum up the expected values of each action across all possible states of nature. This represents the expected profit for that action.

Example:

Consider a decision to invest in a new project. There are two possible states of nature: "Success" and "Failure." The probabilities and profits/losses are as follows:

| State of Nature | Probability | Action A Profit/Loss | Action B Profit/Loss |
|---|---|---|---|
| Success | 0.6 | $10,000 | $5,000 |
| Failure | 0.4 | -$5,000 | -$2,000 |

Calculating Expected Profit for Action A:

- Expected Value (Success) = (Profit x Probability) = $10,000 x 0.6 = $6,000
- Expected Value (Failure) = -$5,000 x 0.4 = -$2,000
- Expected Profit for Action A = $6,000 - $2,000 = $4,000

Calculating Expected Profit for Action B:

- Expected Value (Success) = $5,000 x 0.6 = $3,000
- Expected Value (Failure) = -$2,000 x 0.4 = -$800
- Expected Profit for Action B = $3,000 - $800 = $2,200

Payoff Table:

| State of Nature | Action A | Action B |
|---|---|---|
| Success | $10,000 | $5,000 |
| Failure | -$5,000 | -$2,000 |
| Expected Profit | $4,000 | $2,200 |