Decision Analysis 1: Maximax, Maximin, Minimax Regret

Joshua Emmanuel
11 May 201504:43

TLDRThis video explains decision-making strategies without probabilities. It covers the Maximax (optimistic), Maximin (pessimistic), and Minimax Regret approaches. Using a payoff table, the Maximax strategy suggests investing in stocks for the highest potential profit. Maximin, the conservative approach, advises bonds for the least worst-case scenario. The Minimax Regret method, which calculates the difference between the best possible outcome and the actual one, recommends mutual funds to minimize regret. The video concludes with an invitation to part 2.

Takeaways

  • 📈 Maximax is an optimistic approach where you select the decision alternative with the highest possible payoff.
  • 🛡 Maximin is a conservative approach where you choose the alternative that has the best of the worst outcomes.
  • 🔍 Minimax regret involves choosing the decision alternative with the smallest maximum regret across all possible scenarios.
  • 💼 Decision alternatives are the options available for the decision maker to choose from, such as investing in bonds, stocks, or mutual funds.
  • 🌐 States of nature are the economic conditions that are beyond the control of the decision maker.
  • 💰 Payoffs represent the outcomes of the decisions, which could be profits, costs, distances, times, etc.
  • 🏦 In the given example, the best payoff for stocks is 70, making it the choice under the Maximax approach.
  • 🏗 The worst payoff for bonds is 5, making it the choice under the Maximin approach.
  • 🤔 Regret is calculated as the difference between the best possible payoff and the actual payoff received for a given state of nature.
  • 📊 The regret table is used to determine the maximum regret for each alternative and to identify the alternative with the minimum of these maximum regrets.

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 tool used in decision-making that displays the possible outcomes or payoffs for different decision alternatives under various states of nature or economic conditions.

  • What does the Maximax approach involve?

    -The Maximax approach involves choosing the alternative with the best possible payoff, regardless of the likelihood of different states of nature.

  • How is the Maximin approach different from the Maximax approach?

    -The Maximin approach focuses on choosing the alternative with the best of the worst payoffs, aiming to minimize potential losses, as opposed to the Maximax approach which seeks to maximize potential gains.

  • What is meant by 'regret' in the context of decision-making?

    -In decision-making, 'regret' refers to the opportunity loss, which is the difference between the best possible payoff in a particular state of nature and the actual payoff received.

  • How does the Minimax Regret approach differ from the other two approaches?

    -The Minimax Regret approach involves selecting the alternative with the minimum of all maximum regrets across all states of nature, focusing on minimizing the potential for regret rather than maximizing gains or ensuring against the worst-case scenario.

  • What is the decision based on the Maximax approach if the best payoffs are 45 for bonds, 70 for stocks, and 53 for mutual funds?

    -Based on the Maximax approach, the decision would be to invest in stocks, as it has the highest best possible payoff of 70.

  • What is the decision based on the Maximin approach if the worst payoffs are 5 for bonds, -13 for stocks, and -5 for mutual funds?

    -Based on the Maximin approach, the decision would be to invest in bonds, as it has the highest worst-case payoff of 5.

  • How is the maximum regret calculated for each alternative?

    -The maximum regret for each alternative is calculated by identifying the maximum difference between the best possible payoff in any state of nature and the actual payoff for that alternative.

  • What is the decision based on the Minimax Regret approach if the maximum regrets are 30 for bonds, 18 for stocks, and 17 for mutual funds?

    -Based on the Minimax Regret approach, the decision would be to invest in mutual funds, as it has the lowest maximum regret of 17.

  • Why might a decision-maker choose the Minimax Regret approach over the other two?

    -A decision-maker might choose the Minimax Regret approach to minimize the potential for regret in their decision-making process, aiming to avoid the most significant opportunity losses.

Outlines

00:00

📈 Decision Making Approaches

This video segment introduces three decision-making approaches without considering probabilities: Maximax (optimistic), Maximin (conservative/pessimistic), and Minimax Regret. It explains the use of a payoff table, which lists decision alternatives (investing in bonds, stocks, or mutual funds) and states of nature (economic conditions). Payoffs, which could represent profits, costs, or other metrics, are used to evaluate the alternatives. The Maximax approach selects the alternative with the highest possible payoff, leading to a decision to invest in stocks with the best payoff of 70. The Maximin approach chooses the alternative with the best of the worst payoffs, resulting in a decision to invest in bonds with the highest minimum payoff of 5. The Minimax Regret approach calculates the regret, or opportunity loss, as the difference between the best possible payoff and the actual payoff for each state of nature. It then selects the alternative with the minimum maximum regret, which in this case is mutual funds with a minimum maximum regret of 17.

Mindmap

Keywords

Decision Making

Decision making refers to the process of choosing a course of action among various alternatives. In the context of the video, decision making is approached without considering probabilities, focusing on different strategies to make the best choice. The video discusses how to decide among investment options like bonds, stocks, or mutual funds by evaluating potential outcomes and payoffs.

Maximax

Maximax, also known as the optimistic approach, is a decision-making strategy where one selects the alternative that offers the highest possible payoff. The video illustrates this by choosing to invest in stocks, which has the highest potential profit of 70, representing the best possible outcome among the given options.

Maximin

Maximin, or the conservative approach, is a decision-making strategy where one chooses the alternative that has the best of the worst outcomes. The video uses this strategy to recommend investing in bonds, as it has the highest minimum payoff (5), ensuring a safeguard against the worst-case scenarios.

Minimax Regret

Minimax regret is a decision-making approach that aims to minimize the maximum regret across all possible outcomes. Regret is calculated as the difference between the best possible payoff and the actual payoff received. The video demonstrates this by creating a regret table and choosing mutual funds, which have the lowest maximum regret (17), thus minimizing potential loss from missed opportunities.

Payoff Table

A payoff table, also known as a decision table, is a tool used to display the potential outcomes and their corresponding values (payoffs) for different decision alternatives under various states of nature. 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 discusses 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, also referred to as outcomes, are the conditions or scenarios that are outside 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 decision alternatives.

Payoffs

Payoffs are the values that result from the outcomes of a decision. They can represent profits, costs, distances, times, or other measurable benefits or losses. In the video, payoffs are treated as profits from different investment options under various economic states.

Regret

Regret, in decision-making, is the opportunity loss that occurs when the actual outcome is not as good as the best possible outcome. It is calculated by subtracting the actual payoff from the best possible payoff in a given state of nature. The video explains how to calculate regret for each investment option under different economic conditions to determine the minimax regret strategy.

Conservative Approach

A conservative approach in decision-making is one that prioritizes minimizing potential losses or risks. In the video, the maximin strategy is described as a conservative approach, as it focuses on selecting the alternative with the best worst-case scenario, aiming to protect against significant losses.

Opportunity Loss

Opportunity loss is the potential gain that is forfeited when a decision does not result in the best possible outcome. It is synonymous with regret and is used to evaluate the effectiveness of a decision by comparing it to the ideal scenario. The video discusses opportunity loss in the context of regret to help decide which investment option to choose.

Highlights

Introduction to decision making without probabilities.

Discussion of the Maximax (optimistic) approach.

Explanation of the Maximin (conservative/pessimistic) approach.

Introduction to the Minimax Regret approach.

Description of a payoff table or decision table.

Identification of decision alternatives: bonds, stocks, mutual funds.

Definition of states of nature: economic conditions.

Explanation of payoffs as profits in this example.

Maximax approach leads to a decision to invest in stocks for the highest payoff.

Maximin approach results in a decision to invest in bonds for the best worst-case scenario.

Concept of regret as the difference between best and actual payoff.

Example of calculating regret for different economic conditions.

Construction of a regret table for decision analysis.

Minimax Regret approach chooses the alternative with the minimum of maximum regrets.

Decision to invest in mutual funds based on minimax regret.

Anticipation of part 2 for further discussion.