Decision Analysis 1: Maximax, Maximin, Minimax Regret

Joshua Emmanuel
11 May 201504:43

TLDRThis video introduces three decision-making approaches without the use of probabilities: Maximax (optimistic), Maximin (pessimistic), and Minimax Regret. It explains how to analyze decision alternatives such as investing in bonds, stocks, or mutual funds based on different economic conditions. The Maximax method chooses the highest potential profit, Maximin focuses on minimizing risk by selecting the best of the worst payoffs, and the Minimax Regret approach minimizes potential regret. The video demonstrates these strategies using a payoff table and concludes with a decision based on the minimax regret approach.

Takeaways

  • 📊 Decision making without probabilities focuses on several approaches: Maximax, Maximin, and Minimax Regret.
  • 💡 The Maximax (Optimistic) approach chooses the alternative with the best possible payoff, regardless of risk. In the example, stocks with a payoff of 70 are selected.
  • 🔒 The Maximin (Conservative/Pessimistic) approach focuses on the best of the worst payoffs. Here, bonds with a worst payoff of 5 are selected.
  • 🔄 The Minimax Regret approach seeks to minimize the maximum possible regret across all alternatives.
  • 📉 Regret is calculated as the difference between the best payoff in a state of nature and the actual payoff received for each decision alternative.
  • 📈 In a growing economy, investing in stocks results in no regret, while bonds and mutual funds have regrets of 30 and 17 respectively.
  • 🏛 In a stable economy, investing in bonds has no regret, while stocks have a regret of 15 and mutual funds have no regret.
  • 📉 In a declining economy, bonds have no regret, stocks have a regret of 18, and mutual funds have a regret of 10.
  • 📋 A regret table is used to display the maximum regrets for each alternative.
  • ✅ Based on the Minimax Regret approach, the decision to invest in mutual funds (with the minimum maximum regret of 17) is chosen.

Q & A

  • What is the focus of the video?

    -The video focuses on decision-making methods without using probabilities, specifically discussing the Maximax, Maximin, and Minimax Regret approaches.

  • What is a payoff table or decision table?

    -A payoff table, also known as a decision table, shows decision alternatives in rows and economic conditions in columns, with the values representing payoffs like profit, cost, or time.

  • What are decision alternatives and states of nature?

    -Decision alternatives are the options available to a decision-maker, such as investing in bonds, stocks, or mutual funds. States of nature represent the economic conditions or outcomes that the decision-maker cannot control.

  • How does the Maximax (optimistic) approach work?

    -The Maximax approach selects the alternative with the best possible payoff. For example, in the given scenario, the best payoff is 70 for stocks, so the decision would be to invest in stocks.

  • How does the Maximin (pessimistic) approach work?

    -The Maximin approach selects the alternative with the best of the worst payoffs. In this scenario, bonds have the best worst payoff (5), so the conservative decision would be to invest in bonds.

  • What is the minimax regret approach?

    -The minimax regret approach selects the alternative with the minimum of the maximum regrets. Regret is the difference between the best payoff in a state of nature and the actual payoff received.

  • How is regret calculated in the minimax regret approach?

    -Regret is calculated by subtracting the actual payoff from the best payoff in a given state of nature. For example, if the economy is growing, the best payoff is 70, and if bonds are chosen (with a payoff of 40), the regret is 70 - 40 = 30.

  • What is the regret for investing in mutual funds if the economy is declining?

    -If the economy is declining and mutual funds are chosen, the regret is 5 minus -5, which equals 10.

  • How is the decision made using the minimax regret approach?

    -First, the maximum regret for each alternative is determined. Then, the alternative with the smallest maximum regret is selected. In this case, mutual funds have the smallest maximum regret (17), so the decision is to invest in mutual funds.

  • What is the final decision when using the minimax regret approach in the example provided?

    -The final decision is to invest in mutual funds, as they have the minimum maximum regret of 17.

Outlines

00:00

📊 Introduction to Decision Making without Probabilities

This paragraph introduces the concept of decision-making without probabilities, focusing on various approaches such as the Maximax, Maximin, and Minimax Regret methods. The discussion will cover how decision-makers choose among alternatives such as bonds, stocks, or mutual funds using a payoff table that shows potential profits across different economic conditions.

🔍 Understanding the Payoff Table

This section explains the structure of a payoff table, which lists decision alternatives (bonds, stocks, mutual funds) in rows and states of nature (economic conditions) in columns. The table helps decision-makers evaluate potential payoffs, which could be profit, cost, time, or other factors, depending on the scenario. In this case, payoffs are treated as profits.

😀 Maximax: The Optimistic Approach

In this approach, decision-makers select the alternative with the highest possible payoff, reflecting optimism. For bonds, the best payoff is 45; for stocks, it is 70, and for mutual funds, it is 53. Since stocks offer the highest payoff (70), the optimistic decision would be to invest in stocks.

😐 Maximin: The Conservative Approach

The maximin approach is a pessimistic method where the decision-maker looks at the worst possible outcomes and chooses the alternative with the best of these worst payoffs. Bonds have the worst payoff of 5, stocks -13, and mutual funds -5. Therefore, investing in bonds, which has the best worst-case scenario, is the conservative choice.

🤔 Minimax Regret: Minimizing Opportunity Loss

This approach focuses on minimizing regret, which is the difference between the best possible payoff in a given state of nature and the actual payoff. By comparing regrets for each alternative in various economic conditions, a regret table is constructed. The decision-maker then chooses the alternative with the smallest maximum regret. In this case, mutual funds have the smallest maximum regret (17), so the decision is to invest in mutual funds.

👋 Conclusion: Summary and Next Steps

The video concludes by summarizing the three decision-making approaches (Maximax, Maximin, and Minimax Regret) and highlighting the final decision to invest in mutual funds. Viewers are thanked for watching, and encouraged to stay tuned for the next part of the video series.

Mindmap

Keywords

💡Maximax

The Maximax approach, also known as the optimistic approach, focuses on selecting the alternative with the highest possible payoff, assuming the most favorable conditions. In the video, it suggests investing in stocks, as they have the highest potential profit (70), exemplifying an optimistic decision-making strategy.

💡Maximin

The Maximin approach is a conservative or pessimistic decision-making strategy. It involves selecting the alternative with the best outcome among the worst-case scenarios. In the video, this strategy leads to investing in bonds, as they have the highest minimum payoff (5), highlighting the approach's focus on minimizing potential losses.

💡Minimax Regret

The Minimax Regret approach focuses on minimizing regret by selecting the alternative with the smallest maximum regret. Regret is defined as the difference between the best possible payoff and the actual payoff in a given situation. In the video, this strategy leads to investing in mutual funds, as their maximum regret is the lowest (17).

💡Payoff Table

A payoff table, also called a decision table, presents the possible outcomes (payoffs) of different decision alternatives under various states of nature (economic conditions). In the video, the table lists investments like bonds, stocks, and mutual funds, showing potential profits based on economic conditions.

💡Decision Alternatives

Decision alternatives refer to the different options available to a decision-maker. In the video, the alternatives are investing in bonds, stocks, or mutual funds. These alternatives are evaluated based on their possible payoffs in different economic conditions.

💡States of Nature

States of nature, also known as outcomes, refer to the possible external conditions that affect the payoffs of the decision alternatives. In the video, these are the economic conditions that the decision-maker cannot control but must consider when choosing an investment.

💡Payoffs

Payoffs are the potential results or outcomes (such as profit, cost, or time) of a decision under different states of nature. In the video, the payoffs are treated as profits from investing in bonds, stocks, or mutual funds based on economic conditions.

💡Regret

Regret, also called opportunity loss, is the difference between the best possible payoff in a state of nature and the actual payoff received from a decision. The video explains regret as the lost opportunity, for instance, missing out on the highest profit by choosing a lower-performing investment.

💡Opportunity Loss

Opportunity loss is another term for regret, emphasizing the lost potential when a less-than-optimal decision is made. In the video, it's calculated by comparing the best possible outcome with the actual outcome, like missing the highest profit by choosing bonds over stocks.

💡Economic Conditions

Economic conditions refer to the external factors that influence the payoffs of investment decisions. In the video, these conditions are the states of nature, such as a growing, stable, or declining economy, which affect the profitability of bonds, stocks, and mutual funds.

Highlights

Introduction to decision-making without probabilities.

Three decision-making approaches covered: Maximax, Maximin, and Minimax Regret.

Explanation of a payoff or decision table with decision alternatives and economic conditions.

In the Maximax (optimistic) approach, the decision maker chooses the alternative with the best possible payoff.

In the given example, investing in stocks offers the highest payoff of 70 using the Maximax approach.

The Maximin (conservative or pessimistic) approach involves selecting the alternative with the best of the worst payoffs.

For the Maximin approach, bonds are selected since their worst payoff is 5, the highest among all alternatives' worst outcomes.

The Minimax Regret approach focuses on minimizing the regret, or opportunity loss, across all alternatives.

Regret is calculated as the difference between the best possible payoff in a state of nature and the actual payoff received.

In the case of a growing economy, investing in bonds results in a regret of 30, while investing in stocks leads to no regret.

For a stable economy, investing in stocks incurs a regret of 15.

The Minimax Regret approach involves choosing the alternative with the smallest maximum regret across all states of nature.

In this example, mutual funds are selected as they have the lowest maximum regret of 17.

Each approach provides different perspectives on decision-making based on varying degrees of risk tolerance.

The video concludes with an example applying the Minimax Regret approach, leading to the decision to invest in mutual funds.