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Decision Tree Analysis

  • Overview: A decision tree allows decision makers to analyze choices and their potential outcomes sequentially, helpful in making decisions under risk.

Steps of Decision Tree Analysis

  1. Define the Problem: Clearly understand the issue at hand.

  2. Structure the Decision Tree: Create a visual representation based on a decision table.

  3. Assign Probabilities: Estimate probabilities for each state of nature.

  4. Evaluate Alternatives: For each alternative, assign estimated payoffs based on their outcomes.

  5. Calculate Expected Monetary Values (EMVs): Compute EMVs for each node based on the probabilities and payoffs.

Elements of a Decision Tree

  • Decision Nodes: Illustrated as squares (□), representing choices and alternatives.

    • Example: Tom's Lamber can either:

      • Do nothing

      • Implement a small plan

      • Implement a large plan

  • State of Nature Nodes: Represented by circles (○), indicating possible outcomes of each decision.

    • Example outcomes might include favorable/unfavorable market conditions.

Expected Monetary Value Calculation

  • EMV is calculated by multiplying the probability of each outcome by its corresponding payoff.

  • For example, if a large plan yields:

    • Favorable Market: $200

    • Unfavorable Market: -$180

    • Probability of either market state = 0.5, then:

      • EMV = (0.5 * 200) + (0.5 * -180) = $10

Sequential Decision Making

  • In complex scenarios, decisions may depend on previous choices, visualized effectively through a tree structure.

  • Example with two decisions:

    1. Conduct a market survey (cost: $10,000).

    2. Based on survey results, make decisions for small or large plans based on favorable/unfavorable outcomes.

  • The probabilities derived from this survey will not be perfect; such analyses are influenced by prior probabilities and Bayesian inference.

Cost Analysis in Decision Making

  • Each decision incorporates tangible costs (e.g., a survey cost), affecting the final net payoff.

  • Payoff calculations must reflect these costs for accurate value assessments.

Value of Sample Information

  • The Expected Value of Perfect Information (EVPI) is determined by comparing:

    • The expected value when using sample (or imperfect) information, considering the cost.

    • COin a survey scenario, the results inform decisions under uncertainty but always yield some measure of prediction, never certainty.

  • EVSI = EV with sample information + cost - EV without sample information.

Utility Theory

  • Traditional monetary calculations may not encompass the full value of decisions due to personal preferences or risk tolerances.

  • Utility: A measure that incorporates subjective preferences in decision-making processes.

  • Example: In a gamble:

    • Accept a guaranteed $2 million or gamble for up to $5 million with a chance of losing everything.

  • Rational choices depend on individual risk tolerance; for a risk-averse person, guaranteed amounts may provide higher utility than risking for larger, uncertain payouts.

Conclusion

  • Decision trees facilitate complex decision analysis, especially in sequential scenarios with risks. Using them helps clarify computations of probabilities, outcomes, and personal utility preferences, ultimately guiding effective strategic choices.