Topic 4: Decision AnalysisModule 4.1: Traditional Decision TheoryPessimism and the Maximin Value and Minimax Regret RulesDecision RulesIn what follows we use a running example. Consider a very simple decision problemwhere there are two states and two acts, and where the payoffs are given in the followingtable:VALUE a1 a2 100 0 s1 s2 -50 20The Maximin Value RuleOne of the most popular rules for decision making under uncertainty is based on simplepessimism. The rule, called the maximin value rule, is a rational response in a worldwhere the metaphorical nature is out to get the decision maker.Presuming the payoffs reflect a “good,” the maximin value rule requires the user to firstassign to each act the minimum value that act can receive, and second, to choose the actwith the maximum assigned value. The foregoing example yields the following: First step – the numbers assigned to the acts are –50 and 0, respectively, sincethese are the worst payoffs for each act. Second step – select act #2 because 0 is the larger of the two assigned numbers.In tabular form, we have the following:VALUE a1 a2s1 100 0s2 -50 20Min Value -50 0Max Min Value 0The maximin value rule reflects a kind of pessimism wherein the decision maker viewsnature as being “out to get me,” and thereby minimizes the worst that nature can inflict.Put differently, the maximin value rule reflects a kind of pessimism wherein the decisionmaker always “minimizes the downside risk.” This kind of pessimism is often observedamong people who survived the Great Depression.The Minimax Regret RuleAnother popular rule for decision making under uncertainty is also based on pessimism.Called the minimax regret rule, this rule attempts to model pessimism with moresophistication than the maximin value rule.

The maximin value rule assigns a value to each act without considering the valuesaccruing to the other acts. The Minimax Regret rule avoids this problem by replacing thepayoffs with regret values. The latter, often called opportunity costs, represent regret inthe sense of lost opportunities. Specifically, the regret value that replaces a payoff is thedistance between the payoff and the best payoff possible in the relevant state of nature.The payoff tableVALUE a1 a2 100 0 s1 s2 -50 20yields the regret tableREGRET a1 a2 0 100 s1 s2 70 0The regret values for the first state of nature (s1 = your ticket wins) are calculated asfollows: 0 = 100 - 100 100 = 100 - 0.The regret values for the second state of nature (s2 = your ticket does not win) arecalculated as follows: 70 = 20 – (-50) 0 = 20 – 20.The Minimax Regret rule requires the user to first assign to each act the maximum regretthat act can receive, and second, to choose the act with the minimum assigned regretvalue. The foregoing example yields the following: First step – the numbers assigned to the acts are 70 and 100, respectively, sincethese are the maximum regret values for each act. Second step – select act #1 because 70 is the smaller of the two assigned numbers.In tabular form, we have the following: REGRET a1 a2 0 100 s1 70 0 s2 70 Max Regret 100 70Min Max RegretThe minimax regret rule captures the behavior of individuals who spend their post-decision time regretting their choices. These are the individuals who spend their timesaying “I should have done this and I should have done that.”

PROBLEMS:Find the maximin value and minimax regret acts for the following payoff table:VALUE act 1 act 2 act 3 act 4state 1 -100 -50 10 200state 2 -50 -90 50 100state 3 50 0 -80 -100state 4 100 50 -50 -200Find the minimax cost and minimax regret acts for the following cost table:COST state 1 state 2 state 3act 1 300 400 100act 2 500 700 600act 3 600 300 900Text: Ch. 10, #16

# Topic 4: Decision Analysis Module 4.1: Traditional ...

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**Description: ** Topic 4: Decision Analysis Module 4.1: Traditional Decision Theory Pessimism and the Maximin Value and Minimax Regret Rules Decision Rules In what follows we use a ...

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