Exam 15: Decision Analysis

The following table provides information about the profit payoff of an investment strategy. ​ ​ Decision State of Nature Alternative d1 52 44 44 36 d2 52 68 60 40 d3 36 36 36 44 Probability 0.3 0.2 0.4 0.1 ​ a. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part a? c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?

For a particular maximization problem, the payoff for best decision alternative is $15.7 million while the payoff for one of the other alternatives is $12.9 million. The regret associated with the alternate decision would be

What would be the value added by a market analysis undertaken, if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?

Chance nodes are

The parameter R in an exponential utility function represents

Using the data below, what would be the joint probabilities, P(UÇS_j)? ? Prior Probabilities Conditional Probabilities States of Nature (Sj) P(Sj) P(U\midSj) S1 0.65 0.75 S2 0.20 0.35 S3 0.15 0.20 Total 1.00

A Manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars. ​ Bet on State of Nature (Demand) Stable Down Product A 11 8 8 Product B 8 10 12 ​ ​ The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2 P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5 Use Bayes' theorem to compute the conditional probability of the demand being up, stable, or down, given each market research outcome.

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars). ​ ​ Decision Alternative State of Nature s1 s2 s3 d1 15 40 -20 d2 60 80 -80 ​ ​ The indifference probabilities are as follows: IndifferenceProbability (p) Payoff Decision Maker A Decision Mecision Maker 80 Does not apply Does not apply Does not apply 60 0.7 0.95 0.85 40 0.5 0.9 0.7 15 0.3 0.8 0.55 -20 0.15 0.6 0.35 -80 Does not apply Does not apply Does not apply If P(s₁) = 0.30, P(s₂) = 0.55, and P(s₃) = 0.15, find a recommended decision for each of the three decision makers.

The study of how changes in the probability assessments for the states of nature or changes in the payoffs affect the recommended decision alternative is known as

Choosing a decision alternative that maximizes the minimum profit is a feature of the __________ approach.

Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee). ​ ​ Decision State of Nature Win (\ ) Lose (\ ) Play the game, 50,000 -20,000 Do not play the game, 0 0 ​ a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision. b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R = 6450: -$3000, -$1500, $0, $1500, $3000, $4500, $6000, $7500, $9000.

No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are

Lines showing the alternatives from decision nodes and the outcomes from chance nodes are called

For a minimization problem, the optimistic approach often is referred to as the __________ approach.

__________ refer to the probabilities of the states of nature after revising the prior probabilities based on sample information.

Using the Table below, which is the recommended decision alternative using the optimistic approach? ? Payoff Table Decision Alternative State of Nature 1 State of Nature 2 D1 5 7 D2 -4 1 D3 1 -3 D4 10 2 D5 6 4

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars). ​ Decision Alternative State of Nature s1 s2 s3 d1 15 40 -20 d2 60 80 -80 ​ The indifference probabilities are as follows: Indifference Probability (p) payoff Decision Maker A Decision Maker B Decision Maker C 80 Does not apply Does not apply Does not apply 60 0.7 0.95 0.87 40 0.5 0.9 0.74 15 0.3 0.8 0.59 -20 0.15 0.6 0.37 -80 Does not apply Does not apply Does not apply a. Plot the utility function for money for each decision maker. b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral. c. For the payoff of 40, what is the premium that the risk avoider will pay to avoid risk? What is the premium that the risk taker will pay to have the opportunity of the high payoff?

_____ refers to the probability of one event, given the known outcome of a (possibly) related event.

The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River Basin. The mining company is considering two payment-plan options to buy the mines: I. 100% Payment II. Installment-Payment The payoff received will be based on the quality of coal obtained from the mines which has been categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in million dollars resulting from the various combinations of options and quality are provided below: ​ ​ Payment-Plan Options Quality High Normal Poor Payment 450 320 -250 Installment-Payment 350 300 -110 a. Suppose that management believes that the probability of obtaining High Quality coal is 0.55, probability of Normal Quality Coal is 0.35, and probability of Poor Quality Coal is 0.1. Use the expected value approach to determine an optimal decision. b. Suppose that management believes that the probability of High Quality coal is 0.25, probability of Normal Quality Coal is 0.4, and probability of Poor Quality Coal is 0.35. What is the optimal decision using the expected value approach?