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Three decision makers have assessed utilities for the following decision problem (payoff in dollars): State of...

  1. Three decision makers have assessed utilities for the following decision problem (payoff in dollars):

    State of Nature
    Decision Alternative S1 S2 S3
    d1 10 50 -20
    d2 90 110 -100

    The indifference probabilities are as follows:

    Indifference Probability (p)
    Payoff Decision maker A Decision maker B Decision maker C
    110 1.00 1.00 1.00
    90 0.95 0.80 0.85
    50 0.85 0.70 0.75
    10 0.75 0.55 0.60
    -20 0.60 0.25 0.50
    -100 0.00 0.00 0.00

    Find a recommended decision for each of the three decision makers, if P(s1) = 0.20, P(s2) = 0.60, and P(s3) = 0.20. (Note: For the same decision problem, different utilities can lead to different decisions.) If required, round your answers to two decimal places.

    Decision maker A
    EU(d1) = ?
    EU(d2) = ?
    Recommended decision:

    d2
    Decision maker B
    EU(d1) = ?
    EU(d2) = ?
    Recommended decision:

    d2
    Decision maker C
    EU(d1) = ?
    EU(d2) = ?
    Recommended decision:

    d2

Solutions

Expert Solution

Expected Utility is calculated by as SUMPRODUCT of the indifference probability corresponding to payoff for each decision under each state and the corresponding probability of occurence of each state. For instance, for Decision maker A, EU(d1) = .15*.75+.55*.85+.3*.6 = .76

Part 1.) Decision maker A:
EU(d1) = 0.76
EU(d2) = 0.6925
Recommended decision: d1
Part 2.) Decision maker B
EU(d1) = 0.5425
EU(d2) = 0.67
Recommended decision: d2
Part 3.) Decision maker C
EU(d1) = 0.6525
EU(d2) = 0.6775

Recommended decision: d2

jeff jeffy answered 1 year ago
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