# Decision Analysis 1: Maximax, Maximin, Minimax Regret

TLDRThis video explores decision-making strategies without probabilities, focusing on Maximax (optimistic), Maximin (pessimistic), and Minimax Regret approaches. It uses a payoff table to illustrate how to select the best investment among bonds, stocks, and mutual funds. Maximax suggests investing in stocks for the highest payoff of 70. Maximin, the conservative choice, advises bonds with the least worst payoff of 5. Minimax Regret, which minimizes the maximum regret, points towards mutual funds with the lowest maximum regret of 17.

### Takeaways

- π The video discusses decision-making strategies without relying on probabilities, focusing on Maximax, Maximin, and Minimax Regret approaches.
- πΌ A decision table, also known as a payoff table, is used to outline the decision alternatives and the states of nature with their corresponding payoffs.
- π¦ The Maximax approach, or the optimistic strategy, involves selecting the alternative with the highest possible payoff, leading to the choice of investing in stocks with a best-case profit of 70.
- π‘οΈ The Maximin, or conservative approach, focuses on choosing the alternative with the best of the worst-case scenarios, suggesting an investment in bonds with the highest minimum payoff of 5.
- π€ The Minimax Regret approach calculates the opportunity loss, or regret, as the difference between the best possible payoff and the actual payoff for each state of nature.
- π In the Minimax Regret example, if the economy is growing, the regret for investing in bonds is calculated as 70 - 40 = 30, indicating the loss from not choosing stocks.
- π The regret table is constructed to identify the maximum regret for each alternative, which is crucial for the Minimax Regret decision-making process.
- π For the Minimax Regret strategy, the maximum regrets are 30 for bonds, 18 for stocks, and 17 for mutual funds, with mutual funds being the optimal choice due to the lowest maximum regret.
- β The decision-making process illustrated in the video helps in understanding how to make informed choices under uncertainty by evaluating potential risks and rewards.
- π The video concludes with a teaser for part 2, indicating a continuation of the discussion on decision-making strategies.

### Q & A

### What are the three decision-making approaches discussed in the video?

-The three decision-making approaches discussed in the video are Maximax (optimistic approach), Maximin (conservative or pessimistic approach), and Minimax Regret.

### What is a payoff table or decision table?

-A payoff table or decision table is a visual representation that lists the decision alternatives on the left (rows) and the states of nature or outcomes in the columns, with the values in the table representing payoffs such as profits, costs, distances, or times.

### How does the Maximax approach work?

-The Maximax approach involves selecting the alternative with the best possible payoff. It's an optimistic strategy where the decision-maker chooses the option that offers the highest potential profit.

### What is the Maximin approach and how is it different from Maximax?

-The Maximin approach is a conservative or pessimistic strategy where the decision-maker chooses the alternative with the best of the worst payoffs. It differs from Maximax in that it focuses on minimizing potential losses rather than maximizing gains.

### What does 'states of nature' refer to in the context of decision-making?

-States of nature refer to the various economic conditions or outcomes that are beyond the control of the decision-maker, such as different market scenarios like growing, stable, or declining economy.

### How is regret calculated in the context of the Minimax Regret approach?

-Regret is calculated as the difference between the best possible payoff in a particular state of nature and the actual payoff received if a different decision alternative was chosen.

### What is the Minimax Regret approach and how does it help in decision-making?

-The Minimax Regret approach involves choosing the alternative with the minimum of all maximum regrets across all alternatives. It helps in decision-making by focusing on minimizing the potential regret or opportunity loss.

### What is the decision based on the Maximax approach in the video's example?

-Based on the Maximax approach, the decision is to invest in stocks, as it offers the highest payoff of 70 among the alternatives.

### What is the decision based on the Maximin approach in the video's example?

-Based on the Maximin approach, the decision is to invest in bonds, as it has the best of the worst payoffs, which is 5 among the alternatives.

### What is the decision based on the Minimax Regret approach in the video's example?

-Based on the Minimax Regret approach, the decision is to invest in mutual funds, as it has the minimum of maximum regrets, which is 17 among the alternatives.

### How does the Minimax Regret approach help in handling uncertainty in decision-making?

-The Minimax Regret approach helps in handling uncertainty by focusing on the potential loss of opportunity, thus allowing the decision-maker to minimize the impact of unfavorable outcomes.

### Outlines

### π Decision Making Approaches

This video segment introduces three decision-making approaches without considering probabilities: Maximax, Maximin, and Minimax Regret. The Maximax approach, also known as the optimistic approach, involves selecting the decision alternative with the highest possible payoff, leading to a recommendation to invest in stocks with the best payoff of 70. The Maximin approach, or the conservative/pessimistic method, focuses on choosing the alternative with the best of the worst payoffs, suggesting an investment in bonds with the highest minimum payoff of 5. Lastly, the Minimax Regret approach aims to minimize the maximum regret, which is the opportunity cost of not choosing the best possible alternative. It involves calculating the regret for each state of nature and selecting the alternative with the lowest maximum regret. In this case, mutual funds are recommended as they have the lowest maximum regret of 17.

### Mindmap

### Keywords

### π‘Decision Making

### π‘Maximax

### π‘Maximin

### π‘Minimax Regret

### π‘Payoff Table

### π‘Decision Alternatives

### π‘States of Nature

### π‘Payoffs

### π‘Regret

### π‘Economic Conditions

### π‘Investment

### Highlights

Decision making without probabilities is discussed.

Introduction to Maximax, Maximin, and Minimax Regret decision-making approaches.

Explanation of payoff tables or decision tables in decision analysis.

Decision alternatives are the options available for the decision maker.

Economic conditions are referred to as states of nature or outcomes.

Payoffs represent profits, costs, distances, times, etc., in the decision-making context.

Maximax approach involves choosing the alternative with the best possible payoff.

Maximin approach is about selecting the alternative with the best of the worst payoffs.

Minimax Regret approach focuses on minimizing the maximum regret across all alternatives.

Regret is the difference between the best payoff and the actual payoff received.

Maximax decision is to invest in stocks for the highest payoff.

Maximin decision is to invest in bonds for the best worst-case scenario.

Minimax Regret decision is to invest in mutual funds with the lowest maximum regret.

Regret tables are used to calculate the maximum regret for each alternative.

The decision based on minimax regret minimizes potential losses.

Practical application of decision-making approaches in investment scenarios.

Upcoming part 2 of the video series on decision analysis.