Exam 25: Decision Analysis

A payoff table is shown below. Alternative State of Nature 21 8 -3 12 12 7 -15 9 13 The following prior probabilities are assigned to the states of nature: P( $s _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.7, P( $S _ { 3 }$ ) = 0.1. a. Determine the EMV decision. b. Set up the opportunity loss table. c. Determine the EOL decision. d. What is the expected payoff with perfect information? e. What is the expected value of perfect information?

If EOL( $a _ { 1 }$ ) = $13 000, EOL( $a _ { 2 }$ ) = $25 000 and EOL( $a _ { 3 }$ ) = $20 000, then EOL* = $25 000.

Salaries for employees would be considered a state of nature for a business firm.

We calculate the expected payoff with perfect information (EPPI) by multiplying the probability of each state of nature by the largest payoff associated with that state of nature, and then summing the products.

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below. Payoff Table: Alternative State of Nature 20 28 33 32 29 25 Prior Probabilities: P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6. Likelihood Probabilities: 0.95 0.05 0.08 0.92 a. Determine the EMV decision. b. Set up the opportunity loss table. c. Determine the EOL decision. d. What is the expected payoff with perfect information? e. What is the expected value of perfect information?

Describe how to use a decision tree.

Define the expected value of perfect information (EVPI).

Opportunity loss is the difference between what the decision maker's payoff for an act is and what the payoff would have been had the best decision been made.

Which of the following statements is correct?

The expected value of perfect information (EVPI) is the difference between the expected payoff with perfect information (EPPI) and the expected monetary value (EMV*). That is, EVPI = EPPI - EMV*.

In most business situations, the choice of the best alternative will be made under conditions of:

The expected value of perfect information (EVPI) is always the same as the expected opportunity loss for the best alternative. That is, EVPI = EOL*.

The prior probabilities determine whether or not sample information should be purchased to revise the posterior probabilities associated with the state of nature.

In general, the expected monetary values (EMV) do not represent possible payoffs.

Define expected opportunity loss, EOL.

Which of the following best describes a decision tree?

A payoff table lists the monetary values for each possible combination of:

A high-school student who started doing photography as a hobby is considering going into the photography business. The anticipated payoff table is: Alternative State of Nature Start Do not start new business new business Poor Fair Super -\ 12000 0 \ 10000 0 \ 15000 0 The following prior probabilities are assigned to the states of nature: P(poor) = 0.4, P(fair) = 0.4 , P(super) = 0.2. a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion? b. Convert the payoff table to an opportunity loss table. c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion? d. Review the decisions made in a. and c. Is this a coincidence? Explain. e. What is the expected payoff with perfect information? f. What is the expected value of perfect information? What does it mean?

A payoff table is shown below: Alternative State of Nature 7 0 4 6 2 4 3 5 The following prior probabilities are assigned to the states of nature: P( $s _ { 1 }$ ) = 0.3, P( $S _ { 2 }$ ) = 0.7. a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion? b. Convert the payoff table to an opportunity loss table. c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion? d. What is the expected payoff with perfect information? e. What is the expected value of perfect information?

Which of the following statements is the same as the expected opportunity loss for the best alternative?