Decision Analysis Introduction Chapter 6

What kinds of problems ? Decision Alternatives (“what ifs”) are known States of Nature and their probabilities are known (ex. rainy 20%, partly cloudy 50%, sunny 20%) Outcomes, (referred to as “Payoffs”) are computable under different possible scenarios –each is a combination of a decision alternative and a state of nature

Decision Analysis Basic Terms Decision Alternatives States of Nature (eg. Condition of economy or weather) Payoffs ($ outcome of a choice assuming a state of nature) Criteria (i.e. Expected Value)

Decision Analysis Conditions Certainty –Decision Maker knows with certainty what the state of nature will be - only one possible state of nature Ignorance –Decision Maker knows all possible states of nature, but does not know probability of occurrence Risk –Decision Maker knows all possible states of nature, and can assign probability of occurrence for each state –this will be our focus

Decision Making Under Certainty

Decision Making Under Ignorance – Payoff Table Kelly Construction Payoff Table (Prob. 8-17)

Decision Making Under Ignorance Which alternative will we choose? Maximax –Select the strategy with the highest possible return Maximin –Select the strategy with the smallest possible loss

Maximax: The Optimistic Point of View Select the “best of the best” strategy –Evaluates each decision by the maximum possible return associated with that decision (Note: if cost data is used, the minimum return is “best”) –The decision that yields the maximum of these maximum returns (maximax) is then selected For “risk takers” –Doesn’t consider the “down side” risk –Ignores the possible losses from the selected alternative

Maximax Example Kelly Construction

Maximin: The Pessimistic Point of View Select the “best of the worst” strategy –Evaluates each decision by the minimum possible return associated with the decision –The decision that yields the maximum value of the minimum returns (maximin) is selected For “risk averse” decision makers –A “protect” strategy –Worst case scenario the focus

Maximin Kelly Construction

Decision Making Under Risk Expected Return (ER)* –Select the alternative with the highest expected return –Use a weighted average of the possible returns for each alternative, with probabilities used as weights * Also referred to as Expected Value (EV) or Expected Monetary Value (EMV)

Expected Return Note that we now have probabilities for each state of nature

Expected Value of Perfect Information EVPI measures how much better you could do on this decision if you could always know when each state of nature would occur, where: –EVUPI = Expected Value Under Perfect Information (also called EVwPI, the EV with perfect information, or EV C, the EV “under certainty”) –EVUII = Expected Value of the best action with imperfect information (also called EV Best ) –EVPI = EVUPI – EVUII EVPI tells you how much you are willing to pay for perfect information (or is the upper limit for what you would pay for additional “imperfect” information!)

Expected Value of Perfect Information

Using Excel to Calculate EVPI: Formulas View Kelly Construction