1. Decision Theory Analysis

2. Agenda
Decision Analysis
Problems

3. Decision Analysis Open MGS3100_06Decision_Making.xls
Decision Alternatives
Your options - factors that you have control over
A set of alternative actions - We may chose whichever we please
States of Nature
Possible outcomes – not affected by decision.
Probabilities are assigned to each state of nature
Certainty
Only one possible state of nature
Decision Maker (DM) knows with certainty what the state of nature will be
Ignorance
Several possible states of nature
DM Knows all possible states of nature, but does not know probability of occurrence
Risk
Several possible states of nature with an estimate of the probability of each
DM Knows all possible states of nature, and can assign probability of occurrence for each state

4. Decision Making Under Ignorance
LaPlace-Bayes
All states of nature are equally likely to occur.
Select alternative with best average payoff
Maximax
Evaluates each decision by the maximum possible return associated with that decision
The decision that yields the maximum of these maximum returns (maximax) is then selected
Maximin
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
Minmax Regret
The decision is made on the least regret for making that choice
Select alternative that will minimize the maximum regret

5. LaPlace-Bayes

6. Maximax

7. Maximin

8. MinMax Regret Table
Regret Table: Highest payoff for state of nature – payoff for this decision

9. Decision Making Under Risk
Expected Return (ER) or Expected Value (EV) or Expected Monetary Value (EMV)
Sj The jth state of nature
Di The ith decision
P(Sj) The probability that Sj will occur
Rij The return if Di and Sj occur
ERj The long-term average return
ERi = S Rij  P(Sj)
Variance = S (ERi - Rij)2  P(Sj)
The EMV criterion chooses the decision alternative which has the highest EMV. We'll call this EMV the Expected Value Under Initial Information (EVUII) to distinguish it from what the EMV might become if we later get more information. Do not make the common student error of believing that the EMV is the payoff that the decision maker will get. The actual payoff will be the for that alternative (j) Vi,j and for the State of Nature (i) that actually occurs.

10. Decision Making Under Risk
One way to evaluate the risk associated with an Alternative Action by calculating the variance of the payoffs. Depending on your willingness to accept risk, an Alternative Action with only a moderate EMV and a small variance may be superior to a choice that has a large EMV and also a large variance. The variance of the payoffs for an Alternative Action is defined as
Variance = S (ERi - Rij)2  P(Sj)
Most of the time, we want to make EMV as large as possible and variance as small as possible. Unfortunately, the maximum-EMV alternative and the minimum-variance alternative are usually not the same, so that in the end it boils down to an educated judgment call.

11. Expected Return

12. Expected Value of Perfect Information
EVPI measures how much better you could do on this decision if you could always know what state of nature would occur.
The Expected Value of Perfect Information (EVPI) provides an absolute upper limit on the value of additional information (ignoring the value of reduced risk). It measures the amount by which you could improve on your best EMV if you had perfect information. It is the difference between the Expected Value Under Perfect Information (EVUPI) and the EMV of the best action (EVUII).
The Expected Value of Perfect Information measures how much better you could do on this decision, averaging over repeating the decision situation many times, if you could always know what State of Nature would occur, just in time to make the best decision for that State of Nature. Remember that it does not imply control of the States of Nature, just perfect prediction. Remember also that it is a long run average. It places an upper limit on the value of additional information.

13. Expected Value of Perfect Information
EV with PI - Expected Value with perfect information
S P(Si)  max(Vij)
EVPI = EVw/PI - EMV

14. Expected Value of Perfect Information

15. Agenda
Problems
Decision Analysis

16. What kinds of problems? Alternatives known
States of Nature and their probabilities are known.
Payoffs computable under different possible scenarios

17. Basic Terms Decision Alternatives
States of Nature (eg. Condition of economy)
Payoffs ($ outcome of a choice assuming a state of nature)
Criteria (eg. Expected Value) Z

18. Example Problem 1 - Expected Value & Decision Tree

19. Expected Value

20. Decision Tree