Exam 25: Decision Analysis

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below. Payoff Table: Alternative State of Nature 80 120 9 60 130 170 200 140 100 Prior Probabilities: P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1. Likelihood Probabilities: 0.5 0.3 0.2 0.2 0.6 0.2 0.1 0.2 0.7 A) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ . B) Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*. C) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ . D) Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*. E) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 3 }$ . F) Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*. G) Use your answers to parts a. to f. to calculate the expected monetary value with additional information. H) Calculate the expected value of sample information.

Define the expected payoff with perfect information (EPPI).

The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs and the state-of-nature probabilities.

Which of the following would be considered a state of nature for a business firm?

A company must decide whether or not to change its packaging to a more environmentally safe material. The impact of the decision on profits depends on which of the following three possible scenarios develops in the future. Scenario 1: The media do not focus heavily on concerns about packaging, and no new laws requiring changes in packaging are passed. Under this scenario, the company will make $35 million if they change their packaging now, but will make $75 million if they do not change their packaging now. Scenario 2: The media focus heavily on concerns about packaging, and no new laws requiring changes in packaging are passed. Under this scenario, the company will make $50 million if they change their packaging now, but will make $55 million if they do not change their packaging now. Scenario 3: The media focus heavily on concerns about packaging, and new laws requiring changes in packaging are passed. Under this scenario, the company will make $60 million if they change their packaging now, but will make only $15 million if they do not change their packaging now. The prior probabilities of the three scenarios are 0.3, 0.5 and 0.2, respectively. a. Develop a payoff table for this decision situation. b. What decision will be made to maximise expected payoff? c. What is the most the company should be willing to pay for a research study designed to reduce its uncertainty about media and legal developments concerning packaging? d. Set up the opportunity loss table. e. Which decision has the minimum expected opportunity loss?

Worker safety laws would be considered a state of nature for a business firm.

Which of the following best describes the expected value of sample information (EVSI)?

The number of administration staff to employ would be considered a state of nature for a business firm.

In most business situations, the choice of the best alternative will be made under conditions of risk and ignorance.

Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. Alternative State of Nature (Market condition) \3 0 \2 0 \1 0 \1 9 \2 1 \1 5 \1 1 \2 3 \3 5 Assume that the following probabilities are assigned to the three market conditions: P( $s _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4. a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit? b. Convert the payoff table to an opportunity loss table. c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss? d. Determine the expected payoff that would be realised if perfect information were available. e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

Since the expected monetary value decision is always the same as the expected opportunity loss decision, then EMV*( $a _ { i }$ ) = EOL*( $a _ { i }$ ), for any alternative $a _ { i }$ .