Math Problem Statement

What decision would a pessimist make based on the payoff table provided?

Solution

To determine what decision a pessimist would make, we use the Maximin Criterion. A pessimist focuses on the worst-case scenario for each alternative and chooses the alternative with the highest payoff among those worst-case scenarios.

Here is the payoff table:

AlternativeABCMinimum Payoff (Worst Case)
Alternative 1120140120120
Alternative 22001005050
Alternative 3100120180100
Do Nothing0000

Step-by-Step Process:

  1. Identify the minimum payoff for each alternative:

    • Alternative 1: Minimum = 120
    • Alternative 2: Minimum = 50
    • Alternative 3: Minimum = 100
    • Do Nothing: Minimum = 0
  2. Select the alternative with the highest minimum payoff:

    • The highest among 120, 50, 100, and 0 is 120.

Conclusion:

A pessimist would choose Alternative 1 because it has the highest worst-case payoff.

Would you like me to elaborate further on decision-making criteria or other approaches?


Relative Questions:

  1. How does the Maximin Criterion differ from the Maximax Criterion?
  2. What decision would an optimist make using the given table?
  3. How does incorporating probabilities of each state affect the decision-making process?
  4. What is the impact of adding another alternative with different payoffs?
  5. Can this table be analyzed using expected value if probabilities are assigned?

Tip: The Maximin Criterion is best suited for highly risk-averse decision-makers who prioritize security over potential gains.

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Math Problem Analysis

Mathematical Concepts

Decision Theory
Payoff Tables
Maximin Criterion

Formulas

Maximin Criterion: Choose the alternative with the highest minimum payoff

Theorems

Decision-Making under Uncertainty

Suitable Grade Level

Undergraduate Level or Advanced High School