Question

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.

Answer #1

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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s1
s2
s3
d1
250
100
50
d2
100
75
100
a) Construct a decision tree for this problem.
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buying a computer, leasing a computer, or getting along without a
computer. Based on the information obtained from the firm’s
accountant, the following payoff table (in terms of net profit) was
developed:
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Alternative
S1
S2
S3
A1
4
2
5
A2
8
2
3
A3
3
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6
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