Exam 6: Decision Making Under Uncertainty

In a multistage decision problem, decisions and outcomes alternate. That is, a decision maker makes a decision, then some uncertainty is resolved, then the decision maker makes a second decision, then some further uncertainty is resolved, and so on.

Construct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a newly proposed television program. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

When the lines for two alternatives cross on a strategy region chart, this shows:

Expected monetary value is the weighted sum of the possible monetary outcomes.

(A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. ​ (B) What should the landowner do? Why? ​ (C) Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision? ​ (D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive? ​ (E) What does the risk profile show about the relative risk levels for the landowner's two options? ​ (F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn't feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount -$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences? ​ (G) Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent? ​ (H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist's information is perfectly reliable.

In decision trees, monetary values:

What should the credit union do? What is their expected profit?

Utility function is a function that encodes a person's or company's feelings toward risk.

(A) Construct a decision tree to help the power company decide what to do. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (B) Where should the power company build the plant? What is the expected cost? (C) Suppose that a geologist (and his team) can be hired to analyze the fault structure at Chico Canyon. He will either predict whether an earthquake will occur or not. If the geologist is perfectly reliable, what is the most the company should be willing to pay for his services? (D) Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist's past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions? (E) Should the company hire the geologist if his fee is $1.5M?

The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars. Audience -The station is most uncertain about the average monthly revenue associated with the rock format and an A1 audience. Construct a strategy region chart for this input variable with a possible range from $85,000 to $200,000. Does the optimal decision to select the country format change at any point in this range?

The expected value of perfect information (EVPI) is irrelevant concept since perfect information is almost never available at any price.

In decision trees, a probability node (a circle) is a time when the decision maker makes a decision.

In a single-stage decision tree problem, you make ____ first and then all you wait to see a(n) ____.

Construct a decision tree to help the credit union decide whether or not to make the loan. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

With regard to decision making, most individuals are ____.

PrecisionTree tornado and spider charts are:

What should the network do? What is their expected profit?

(A) Construct a decision tree to help her model her option decision making. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (B) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years? (C) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs) (D) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV?

The expected monetary value (EMV) criterion is sometimes referred to as "playing the averages".

(A) Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (B) What is the best lease option? Why? (C) Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision. If the mechanic is always correct in his assessments, what is the most the company would pay for the inspection?