Math Problem Statement
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:
Alternative | A | B | C | Minimum Payoff (Worst Case) |
---|---|---|---|---|
Alternative 1 | 120 | 140 | 120 | 120 |
Alternative 2 | 200 | 100 | 50 | 50 |
Alternative 3 | 100 | 120 | 180 | 100 |
Do Nothing | 0 | 0 | 0 | 0 |
Step-by-Step Process:
-
Identify the minimum payoff for each alternative:
- Alternative 1: Minimum = 120
- Alternative 2: Minimum = 50
- Alternative 3: Minimum = 100
- Do Nothing: Minimum = 0
-
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:
- How does the Maximin Criterion differ from the Maximax Criterion?
- What decision would an optimist make using the given table?
- How does incorporating probabilities of each state affect the decision-making process?
- What is the impact of adding another alternative with different payoffs?
- 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
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