Decision Analysis 1: Maximax, Maximin, Minimax Regret

Joshua Emmanuel
11 May 201504:43

TLDRThis video explores decision-making strategies without probabilities, focusing on Maximax (optimistic), Maximin (pessimistic), and Minimax Regret approaches. It introduces a payoff table with decision alternatives and states of nature. The Maximax strategy advises investing in stocks for the best payoff of 70. Maximin, the conservative approach, suggests bonds with the best worst-case scenario of 5. Minimax Regret, considering the opportunity loss, recommends mutual funds with the minimum maximum regret of 17, guiding decision-makers to minimize potential regret.

Takeaways

  • 📊 Decision making without probabilities can be approached using various strategies: Maximax, Maximin, and Minimax Regret.
  • 🚀 The Maximax approach, or the optimistic strategy, involves selecting the decision alternative with the highest possible payoff.
  • 🛡 The Maximin approach, also known as the conservative or pessimistic strategy, focuses on choosing the alternative with the best of the worst possible outcomes.
  • 💡 The Minimax Regret approach aims to minimize the maximum regret, which is calculated as the difference between the best possible payoff and the actual payoff received.
  • 💼 In the provided example, the decision alternatives are investing in bonds, stocks, or mutual funds, with payoffs represented as profits.
  • 📈 The Maximax decision is to invest in stocks, as it offers the highest payoff of 70.
  • 📉 The Maximin decision is to invest in bonds, as it has the highest minimum payoff (best of the worst) of 5.
  • 🔍 To calculate regret, one must compare the actual payoff with the best possible payoff under each economic condition.
  • 📋 The regret table is a useful tool to visualize the maximum regret for each alternative and to aid in decision-making.
  • 🏦 The Minimax Regret decision is to invest in mutual funds, as it has the lowest maximum regret of 17 among the alternatives.
  • 🔜 This video is part 1 of a series, with part 2 expected to delve deeper into decision analysis techniques.

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 the minimax regret approach.

  • What is the purpose of a payoff table in decision-making?

    -A payoff table, also known as a decision table, is used to display the possible outcomes or payoffs for each decision alternative under different states of nature, helping the decision-maker to evaluate and choose the best course of action.

  • How does the Maximax approach determine the best decision?

    -The Maximax approach identifies the best decision by choosing the alternative with the highest possible payoff across all states of nature.

  • What is the rationale behind the Maximin approach?

    -The Maximin approach is a conservative strategy that selects the alternative with the best of the worst possible outcomes, aiming to minimize potential losses.

  • Can you explain the concept of regret in the context of decision-making?

    -Regret, or opportunity loss, is the difference between the best possible payoff in a given state of nature and the payoff received from the chosen alternative. It represents the loss incurred by not choosing the optimal alternative in hindsight.

  • How does the minimax regret approach differ from the other two approaches?

    -The minimax regret approach focuses on minimizing the maximum regret across all alternatives, rather than maximizing payoffs or minimizing the worst-case scenario. It seeks to minimize the potential for regret by choosing the alternative with the lowest maximum regret.

  • What is the decision recommended by the Maximax approach in the video's example?

    -According to the Maximax approach, the recommended decision in the video's example is to invest in stocks, as it offers the highest possible payoff of 70.

  • What alternative does the Maximin approach suggest based on the video?

    -The Maximin approach suggests investing in bonds, as it has the best of the worst payoffs, which is 5.

  • What is the decision made using the minimax regret approach in the video?

    -Using the minimax regret approach, the decision is to invest in mutual funds, as it has the lowest maximum regret of 17.

  • How is the maximum regret calculated for each alternative in the minimax regret approach?

    -The maximum regret for each alternative is calculated by identifying the highest regret value among all states of nature for that alternative. This represents the worst-case scenario of regret for each decision.

  • What is the significance of the decision table in evaluating different decision-making strategies?

    -The decision table is significant as it provides a structured way to compare the outcomes of different decision-making strategies by clearly presenting the payoffs and regrets associated with each alternative under various conditions.

Outlines

00:00

📊 Decision Making Approaches

This video segment introduces three decision-making approaches without considering probabilities: Maximax (optimistic), Maximin (pessimistic), and Minimax Regret. It explains the use of a payoff table, which includes decision alternatives like investing in bonds, stocks, or mutual funds, and states of nature such as economic conditions. The Maximax approach advocates for choosing the alternative with the highest possible payoff, leading to a decision to invest in stocks with the best payoff of 70. Conversely, the Maximin approach suggests selecting the alternative with the best worst-case scenario, resulting in a recommendation to invest in bonds with the highest minimum payoff of 5. The Minimax Regret approach focuses on minimizing the maximum regret, which is the difference between the best possible payoff and the actual payoff received. By calculating the maximum regret for each alternative and choosing the one with the lowest maximum regret (17 for mutual funds), the video concludes that investing in mutual funds is the preferred decision under this approach.

Mindmap

Keywords

💡Decision Making

Decision making refers to the process of selecting a course of action among various alternatives. In the context of the video, it is about choosing the best investment option without considering probabilities. The video discusses different approaches to decision making, emphasizing rational strategies to make the most informed choice.

💡Maximax

Maximax, also known as the optimistic approach, is a decision-making strategy where one chooses the alternative that offers the highest possible payoff. The video illustrates this by selecting stocks as the best investment, which has the highest potential profit of 70, assuming the best-case scenario.

💡Maximin

Maximin, or the conservative approach, is a decision-making strategy where one chooses the alternative that has the best outcome among the worst possible scenarios. The video uses this approach to recommend investing in bonds, which has the highest minimum payoff of 5, ensuring a safer choice in pessimistic scenarios.

💡Minimax Regret

Minimax regret is a decision-making approach that aims to minimize the maximum regret, which is the difference between the best possible outcome and the actual outcome. The video demonstrates this by calculating the maximum regret for each investment option and choosing mutual funds, which has the lowest maximum regret of 17.

💡Payoff Table

A payoff table, or decision table, is a tool used to display the potential outcomes or payoffs of different decision alternatives under various conditions. In the video, the payoff table is used to compare the profits from investing in bonds, stocks, or mutual funds under different economic conditions.

💡Decision Alternatives

Decision alternatives are the options available for a decision maker to choose from. The video presents three alternatives: investing in bonds, stocks, or mutual funds. Each alternative has its own set of payoffs associated with different economic conditions.

💡States of Nature

States of nature, or outcomes, are the conditions or circumstances that are beyond the control of the decision maker. In the video, these include different economic conditions such as growing, stable, or declining economy, which affect the payoffs of the investment alternatives.

💡Payoffs

Payoffs are the outcomes or results of a decision, often represented as profits, costs, or other measurable values. In the video, payoffs are the profits that could be earned from the different investment options under various economic states.

💡Regret

Regret, or opportunity loss, is the feeling of disappointment from not choosing the best possible option. In decision analysis, it is quantified as the difference between the best possible payoff and the actual payoff received. The video calculates regret for each investment under different economic conditions to guide decision making.

💡Economic Conditions

Economic conditions are the prevailing market or financial circumstances that can influence the performance of investments. The video considers three economic conditions: growing, stable, and declining economy, each affecting the potential profits from investing in bonds, stocks, or mutual funds.

💡Investment

Investment in this context refers to the act of putting money into financial assets like bonds, stocks, or mutual funds with the expectation of earning a return. The video discusses how to make investment decisions using various decision-making strategies to maximize profits or minimize risks.

Highlights

Decision making without probabilities is discussed.

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

Explanation of a payoff table or decision table 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.

Maximax approach chooses the alternative with the best possible payoff.

Maximin approach selects the alternative with the best of the worst payoffs.

Minimax Regret approach minimizes the maximum regret across all alternatives.

Regret is the difference between the best and actual payoff in a state of nature.

Maximax decision is to invest in stocks with the best payoff of 70.

Maximin decision is to invest in bonds with the best worst-case payoff of 5.

Minimax Regret decision is to invest in mutual funds with the minimum maximum regret of 17.

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

The decision based on minimax regret involves choosing the alternative with the lowest maximum regret.

The video concludes with a teaser for part 2.

Thanks for watching and an invitation to the next part of the series.