If the decisionmaker makes her decision based on the minimax regret approach, what is the maximum regret associated with this decision?

Question

BlackTom AI · Accepted Answer

The question asks about the minimax regret decision rule and the maximum regret associated with the chosen decision.
First, recall how minimax regret works: for each possible decision, you compute the regret in every state of the world. Regret in a state is the difference between the payoff of the best possible decision in that state and the payoff actually obtained by the chosen decision in that state. Then, for each decision, you take the worst (maximum) regret across all states. Finally, you select the decision that minimizes this worst-case regret (the minimax regret choice).
In order to determine the maximum regret for a particular decision, you would:
- identify all possible states of the world relevant to the decision, if not already listed,
- determine the payoff of the best possible decision in each state,
- subtract the payoff of the chosen decision from that best payoff to obtain the regret in each state,
- find the largest of these regrets across all states for that decision.
If the provided answer data indicates a value of 120, that would imply that, under the minimax regret computation for the given scenario, the largest regret associated with the decision in question equals 120. In other words, in at least one state, the difference between the best achievable payoff and the payoff of this decision is 120, and this is the maximum regret across all states for this decision.
Note: Since the question text does not include the actual payoff matrix, the specific per-state regrets cannot be shown here. The general procedure above describes how the 120 would be obtained if the state-by-state payoffs were available. If you had the full payoff table, you would calculate regrets for each state, identify the maximum for that decision, and then compare those maxima across all candidate decisions to find the minimax regret choice.

If the decisionmaker makes her decision based on the minimax regret approach, what is the maximum regret associated with this decision?Numerical

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