Assignment Choice under Uncertainty

Published by Mario Oettler on

Last Updated on 28. April 2023 by Martin Schuster

Task

We have four alternatives A1, A2, A3, and A4 to choose from. There are also four situations S1, S2, S3, and S4 that cause different pay-offs for each alternative. Furthermore, the probability of occurrence of those four situations is unknown.

 S1S2S3S4
A1101058
A2910128
A31532-2
A414430

What alternative should you select under the following decision rules:

  • LaPlace rule?
  • Maxmin-rule
  • Maximax rule
  • Range rule (lowest rank = 1)
  • Minimax regret rule
  • Hurzwicz rule (optimism parameter a = 0.3)

Solution

S1S2S3S4LaPlaceMaximin RuleMaximax ruleRange ruleMinimax RegrettHurwicz
A11010588.25510776.5
A29101289.75812769.2
A31532-24.5-21511103.1
A4144305.25014984.2

The bold numbers show the choice for each rule.

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