Question

# Suppose a decision maker is considering three decision alternatives: A1, A2, and A3. Three potential states...

Suppose a decision maker is considering three decision alternatives: A1, A2, and A3. Three potential states of nature have been identified: S1, S2, and S3. The payoff for each combination of alternative and state of nature has been estimated and appears in the following payoff table:

 S1 S2 S3 A1 113 96 -65 A2 117 62 -52 A3 32 45 40

Calculate the regret (or opportunity loss) value for the combination of A2 and S2.

We first need to understand that this is a payoff table and to find the regret of all the alternatives and states, we need to follow the maximin approach in which for each state S, we need to find the maximum value, and then subtract that from the value of each alternative to find the regret of choosing that option

 S1 S2 S3 A1 113 96 -65 A2 117 62 -52 A3 32 45 40

For S1, highest payoff is 117; For S2, highest payoff is 96; For S3, highest payoff is 40

 S1 S2 S3 A1 113 -117 = -4 96-96 = 0 -65 -40 = -105 A2 117-117 = 0 62 -96 = -34 -52 -40 = -92 A3 32-117= -85 45 -96 = -51 40 -40 = 0

So as calculated in the table above, the regret (or opportunity loss) value for the combination of A2 and S2 is -34

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