1. Chapter 19 Decision Making
Yandell – Econ 216

2. Chapter Goals After completing this chapter, you should be able to:
Describe the decision environments of certainty and uncertainty
Construct a payoff table and an opportunity-loss table
Define and apply the expected value criterion for decision making
Compute the value of perfect information
Develop and use decision trees for decision making
Yandell – Econ 216

3. Start Here
You should begin this chapter with the overview material found here
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Yandell – Econ 216

4. Decision Making Overview
Decision Environment
Decision Criteria
Certainty
Nonprobabilistic
Uncertainty
Probabilistic
Yandell – Econ 216

5. The Decision Environment
Certainty: The results of decision alternatives are known *
Certainty
Example:
Must print 10,000 color brochures
Offset press A: $2,000 fixed cost
+ $.24 per page
Offset press B: $3,000 fixed cost
+ $.12 per page
Uncertainty
Yandell – Econ 216

6. The Decision Environment
(continued)
Uncertainty: The outcome that will occur after a choice is unknown
Decision Environment
Certainty
Example:
You must decide to buy an item now or wait. If you buy now the price is $2,000. If you wait the price may drop to $1,500 or rise to $2,200. There also may be a new model available later with better features. *
Uncertainty
Yandell – Econ 216

7. * Decision Criteria Decision Criteria
Nonprobabilistic Decision Criteria: Decision rules that can be applied if the probabilities of uncertain events are not known. *
Nonprobabilistic
maximax criterion
maximin criterion
minimax regret criterion
Probabilistic
Yandell – Econ 216

8. * Decision Criteria Decision Criteria
(continued)
Decision Criteria
Probabilistic Decision Criteria: Consider the probabilities of uncertain events and select an alternative to maximize the expected payoff of minimize the expected loss
Nonprobabilistic *
Probabilistic
maximize expected value
minimize expected opportunity loss
Yandell – Econ 216

9. Features of Decision Making
List Alternative Courses of Action (Possible Events or Outcomes)
Determine ‘Payoffs’ (Associate a Payoff with Each Event or Outcome)
Adopt Decision Criteria (Evaluate Criteria for Selecting the Best Course of Action)
Yandell – Econ 216

10. List Possible Actions or Events
Two Methods of Listing
Payoff Table
Decision Tree
Yandell – Econ 216

11. A Payoff Table
A payoff table shows alternatives, states of nature, and payoffs
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Yandell – Econ 216

12. Maximax Solution The maximax criterion (an optimistic approach):
For each option, find the maximum payoff
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20 1.
Maximum Profit
200
120 40
Yandell – Econ 216

13. Greatest maximum is to choose Large factory
Maximax Solution
(continued)
The maximax criterion (an optimistic approach):
For each option, find the maximum payoff
Choose the option with the greatest maximum payoff
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20 2.
Greatest maximum is to choose Large factory 1.
Maximum Profit
200
120 40
Yandell – Econ 216

14. Maximin Solution The maximin criterion (a pessimistic approach):
For each option, find the minimum payoff
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20 1.
Minimum Profit
-120
-30 20
Yandell – Econ 216

15. Greatest minimum is to choose Small factory
Maximin Solution
(continued)
The maximin criterion (a pessimistic approach):
For each option, find the minimum payoff
Choose the option with the greatest minimum payoff
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20 2.
Greatest minimum is to choose Small factory 1.
Minimum Profit
-120
-30 20
Yandell – Econ 216

16. Opportunity Loss
Opportunity loss is the difference between an actual payoff for a decision and the optimal payoff for that state of nature
Payoff Table
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
The choice “Average factory” has payoff 90 for “Strong Economy”. Given “Strong Economy”, the choice of “Large factory” would have given a payoff of 200, or 110 higher. Opportunity loss = 110 for this cell.
Yandell – Econ 216

17. Opportunity Loss in $1,000’s
(continued)
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Payoff Table
Opportunity Loss Table
Investment Choice
(Alternatives)
Opportunity Loss in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
110
160 70 90
140 50
Yandell – Econ 216

18. Minimax Regret Solution
The minimax regret criterion:
For each alternative, find the maximum opportunity loss (or “regret”)
Opportunity Loss Table
Investment Choice
(Alternatives)
Opportunity Loss in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
110
160 70 90
140 50 1.
Maximum Op. Loss
140
110
160
Yandell – Econ 216

19. Minimax Regret Solution
(continued)
The minimax regret criterion:
For each alternative, find the maximum opportunity loss (or “regret”)
Choose the option with the smallest maximum loss
Opportunity Loss Table
Investment Choice
(Alternatives)
Opportunity Loss in $1,000’s
(States of Nature)
Strong Economy
Stable Economy
Weak Economy
Large factory
Average factory
Small factory
110
160 70 90
140 50 1.
Maximum Op. Loss 2.
Smallest maximum loss is to choose Average factory
140
110
160
Yandell – Econ 216

20. Expected Value Solution
The expected value is the weighted average payoff, given specified probabilities for each state of nature
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Suppose these probabilities have been assessed for these states of nature
Yandell – Econ 216

21. Expected Value Solution
(continued)
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Maximize expected value by choosing Average factory
Expected Values 61 81 31
Example: EV (Average factory) = 90(.3) + 120(.5) + (-30)(.2)
= 81
Yandell – Econ 216

22. Expected Opportunity Loss Solution
Opportunity Loss Table
Investment Choice
(Alternatives)
Opportunity Loss in $1,000’s
(States of Nature)
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Large factory
Average factory
Small factory
110
160 70 90
140 50
Minimize expected op. loss by choosing Average factory
Expected Op. Loss
(EOL) 63 43 93
Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2)
= 63
Yandell – Econ 216

23. Value of Information
Expected Value of Perfect Information, EVPI (also called Cost of Uncertainty)
Expected Value of Perfect Information
= Expected Value Under Certainty (EVUC)
– Expected Value without information (EV)
so: EVPI = EVUC – EV
Yandell – Econ 216

24. Expected Value Under Certainty
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Expected Value Under Certainty (EVUC):
EVUC = expected value of the best decision, given perfect information
Example: Best decision given “Strong Economy” is “Large factory”
Yandell – Econ 216

25. Expected Value Under Certainty
(continued)
Investment Choice
(Alternatives)
Profit in $1,000’s
(States of Nature)
Strong Economy
(.3)
Stable Economy
(.5)
Weak Economy
(.2)
Large factory
Average factory
Small factory
200 90 40 50
120 30
-120
-30 20
Now weight these outcomes with their probabilities to find EVUC:
EVUC = 200(.3)+120(.5)+20(.2)
= 124
Yandell – Econ 216

26. Value of Information Solution
Expected Value of Perfect Information (EVPI)
= Expected Value Under Certainty (EVUC)
– Expected Value without information (EV)
Recall: EVUC = 124
EV is maximized by choosing “Average factory”,
where EV = 81
so: EVPI = EVUC – EV
= 124 – 81
= 43
Yandell – Econ 216

27. Decision Tree Analysis
A Decision tree shows a decision problem, beginning with the initial decision and ending will all possible outcomes and payoffs.
Use a square to denote decision nodes
Use a circle to denote uncertain events
Yandell – Econ 216

28. Sample Decision Tree Large factory Average factory Small factory
Strong Economy
Large factory
Stable Economy
Weak Economy
Strong Economy
Average factory
Stable Economy
Weak Economy
Strong Economy
Small factory
Stable Economy
Weak Economy
Yandell – Econ 216

29. Add Probabilities and Payoffs
(continued)
Strong Economy
(.3)
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy 90
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
Decision
(.3)
Strong Economy 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Uncertain Events
(States of Nature)
Probabilities
Payoffs
Yandell – Econ 216

30. Fold Back the Tree Large factory Average factory Small factory
Strong Economy
(.3)
EV=200(.3)+50(.5)+(-120)(.2)=61
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy
EV=90(.3)+120(.5)+(-30)(.2)=81 90
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
(.3)
Strong Economy
EV=40(.3)+30(.5)+20(.2)=31 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Yandell – Econ 216

31. Make the Decision Large factory Average factory Small factory
Strong Economy
(.3)
EV=61
200
Large factory
Stable Economy
(.5) 50
Weak Economy
(.2)
-120
(.3)
Strong Economy
EV=81 90
Maximum
EV=81
Average factory
(.5)
Stable Economy
120
(.2)
Weak Economy
-30
(.3)
Strong Economy
EV=31 40
Small factory
(.5)
Stable Economy 30
(.2)
Weak Economy 20
Yandell – Econ 216

32. Utility
Utility is the pleasure or satisfaction obtained from an action.
Note: The utility of an outcome may not be the same for each individual.
Yandell – Econ 216

33. Utility
Example: each incremental $1 of profit does not have the same value to every individual:
A risk averse person, once reaching a goal, assigns less utility to each incremental $1.
A risk seeker assigns more utility to each incremental $1.
A risk neutral person assigns the same utility to each extra $1.
Yandell – Econ 216

34. Maximizing Expected Utility
Making decisions in terms of utility, not $
Translate $ outcomes into utility outcomes
Calculate expected utilities for each action
Choose the action to maximize expected utility
Yandell – Econ 216

35. Assessing Attitudes about Risk
What is your risk preference?
Risk averse?
Risk neutral?
Risk loving?
Tools exist to assess your attitude toward risk
Classroom assessment if time permits
Yandell – Econ 216

36. Rationality: Making a Good Decision
A good decision does not guarantee a good outcome
A good outcome does not necessarily indicate a good decision
Yandell – Econ 216

37. practice problem pdf file
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Yandell – Econ 216

38. Chapter Summary Examined decision making environments
certainty and uncertainty
Reviewed decision making criteria
nonprobabilistic: maximax, maximin, minimax regret
probabilistic: expected value, expected opp. loss
Computed the Value of Perfect Information (EVPI)
Developed decision trees and applied them to decision problems
Yandell – Econ 216