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Exam 13: Decision Analysis

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Question 1

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If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =

A) .10
B) .27
C) .30
D) .55

E) A) and B)
F) None of the above

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Question 2

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How can a good decision maker "improve" luck?

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A good decision maker can "improve" luck...

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Question 3

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Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.

If p is the probability of Event 1 and (1-p) is the probability of Event 2, for what values of p would you choose A? B? C? Values in the table are payoffs. $\begin{array} { c c c } \text { Choice/Event } & \text { Event 1 } & \text { Event 2 } \\\hline \text { A } & 0 & 20 \\\text { B } & 4 & 16 \\\text { C } & 8 & 0\end{array}$

Square nodes in a decision tree indicate that a decision must be made.

For a maximization problem, the conservative approach is often referred to as the

Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.

Making a good decision

Sensitivity analysis considers

The expected value of an alternative can never be negative.

The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do. $\begin{array} { c | r r r } & & { \text { State of Nature } } \\\text { Decision } & s _ { 1 } & s _ { 2 } & s _ { 3 } \\\hline d _ { 1 } & 30 & 80 & - 30 \\d _ { 2 } & 100 & 30 & - 40 \\d _ { 3 } & - 80 & - 10 & 120 \\d _ { 4 } & 20 & 20 & 20\end{array}$ a.if an optimistic strategy is used. b.if a conservative strategy is used. c.if minimax regret is the strategy.

A decision tree

States of nature should be defined so that one and only one will actually occur.

The options from which a decision maker chooses a course of action are

EVPI equals the expected regret associated with the minimax decision.

A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs $\begin{array} { c | ccc } & { \text { State of Nature } } \\\text { Decision } & \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\\hline \mathrm { d } _ { 1 } & 5 & 10 & 20 \\\mathrm {~d} _ { 2 } & - 25 & 0 & 50 \\\mathrm {~d} _ { 3 } & - 50 & - 10 & 80 \\\hline \text { Probability } & .30 & .35 & .35\end{array}$ Rank the decision alternatives on the basis of expected value.

Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.

Explain why the decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available.

For the payoff table below, the decision maker will use P(s₁) = .15, P(s₂) = .5, and P(s₃) = .35. $\begin{array} { c | r r c } &{ \text { State of Nature } } \\\text { Decision } & { \mathrm { s } _ { 1 } } & { \mathrm { s } _ { 2 } } & \mathrm {~s} _ { 3 } \\\hline d _ { 1 } & - 5,000 & 1,000 & 10,000 \\d _ { 2 } & - 15,000 & - 2,000 & 40,000\end{array}$ What alternative would be chosen according to expected value?

States of nature