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BU-25 Lecture

Intro to Decision Analysis

Payoff Tables and Decision Making under Uncertainty

You have the opportunity to co-op for a fried’s start-up, working part-time or full-time and even invest

in the company.

States of Nature

Company Takes Off

Company does bad

Alternatives

Part Time

40,000

20,000

Full Time

70,000

10,000

Full Time and

Investment

110,000

-10,000

• The choices you have are called alternatives. The outcomes are determined by states of nature

and each combo has a payoff

• If we can assign probabilities to the states of nature (events), then we can use expected value

calculations.

o Unfortunately, we may not have any idea what probabilities to assign, even if you have

historical (empirical) data, it may not be applicable in your case

Decision Making without Probabilities

• Decision Criteria:

o Maximax (optimistic)

▪ Find the best payoff by alternative

▪ Pick the highest best case

o Maximin (pessimistic)

▪ Find the worst payoff by alternative, and pick the highest (worst case)

▪ Safest choice

o Minimax Regret

▪ First, we need a regret table, built by finding the best payoff by state of nature,

the calculating regret in $ for the other payoffs

▪ What you could have had minus what you have = regret

▪ By alternative, find the largest regret, then pick the option whose worst-case

regret is the smallest

• Substitutes for Probabilities

o Equal likelihood criterion

▪ Here use 50% for each and calculate the expected value

o Hurwicz Criterion

▪ Use α, a oeffiiet of optiis α= is optiisti, α= is pessiisti

▪ Assign α to best case, and 1-α to the worst case

▪ Ex. α=0.4, Best case*(0.4)+Worst case*(0.6)=Expected Value

• Decision Making with Probabilities:

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