1. Chapter Topics The Payoff Table and Decision Trees Opportunity Loss
Criteria for Decision Making
Expected Monetary Value
Return to Risk Ratio

2. 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)

3. List Possible Actions or Events
Two Methods of Listing
Payoff Table
Decision Tree

4. Payoff Table
Consider a food vendor determining whether to sell soft drinks or hot dogs.
Course of Action (Aj)
Sell Soft Drinks (A1)
Sell Hot Dogs (A2)
Event (Ei)
Cool Weather (E1) x11 =$ x12 = $100
Warm Weather (E2) x21 = x22 = 125
xij = payoff (profit) for event i and action j

5. Decision Tree:Example
Food Vendor Profit Tree Diagram
x11 = $50
Cool Weather
Warm Weather
Soft Drinks
x21 = 200
Hot Dogs
x12 = 100
Cool Weather
Warm Weather
x22 =125

6. Opportunity Loss: Example
Highest possible profit for an event Ei Actual profit obtained for an action Aj
Opportunity Loss (lij )
Event: Cool Weather
Action: Soft Drinks Profit: $50
Alternative Action: Hot Dogs Profit: $100
Opportunity Loss = $100 - $50 = $50
Note: Opportunity Loss is always positive

7. Opportunity Loss: Table
Alternative Course of Action
Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action
Cool Hot = = 0 Weather Dogs
Warm Soft = = 75 Weather Drinks

8. Decision Criteria Expected Monetary Value (EMV)
The expected profit for taking an action Aj
Expected Opportunity Loss (EOL)
The expected loss for not taking action Aj
Expected Value of Perfect Information (EVPI)
The expected opportunity loss from the best decision

9. Decision Criteria -- EMV
Expected Monetary Value (EMV)
Sum (monetary payoffs of events) ´ (probabilities of the events) N å
EMVj =
Xij Pi
i = 1
EMVj = expected monetary value of action j
xi,j = payoff for action j and event i
Pi = probability of event i occurring

10. Decision Criteria -- EMV Table Example: Food Vendor
Pi Event Soft xijPi Hot xijPi
Drinks Dogs
Cool $ $50 ´.5 = $ $ $100´.50 = $50
.50 Warm $ $200 ´.5 = $ $25´.50 = 62.50
EMV Soft Drink = $125
EMV Hot Dog = $112.50
Better alternative

11. Decision Criteria -- EOL
Expected Opportunity Loss (EOL)
Sum (opportunity losses of events) ´ (probabilities of events) N å
EOLj =
lij Pi
i =1
EOLj = expected monetary value of action j
li,j = payoff for action j and event i
Pi = probability of event i occurring

12. Decision Criteria -- EOL Table Example: Food Vendor
Pi Event Op Loss lijPi OP Loss lijPi
Soft Drinks Hot Dogs
Cool $ $50´.50 = $ $0 $0´.50 = $0
Warm $0 ´.50 = $ $75 $75 ´.50 = $37.50
EOL Soft Drinks = $25
EOL Hot Dogs = $37.50
Better Choice

13. Decision Criteria -- EVPI
Expected Value of Perfect Information (EVPI)
The expected opportunity loss from the best decision
Represents the maximum amount you are willing
to pay to obtain perfect information
Expected Profit Under Certainty Expected Monetary Value of the Best Alternative
EVPI (should be a positive number)

14. EVPI Computation Expected Profit Under Certainty
= .50($100) + .50($200)
= $150
Expected Monetary Value of the Best Alternative
= $125
EPVI = $25
The maximum you would be willing to spend to obtain perfect information.

15. Taking Account of Variability: FoodVendor
s2 for Soft Drink
= ( )2 ´.5 + ( )2 ´.5 = 5625
s for Soft Drink = 75
CVfor Soft Drinks = (75/125) ´ 100% = 60%
s2 for Hot Dogs = s for Hot dogs = 12.5
CVfor Hot dogs = 11.11%

16. Return to Risk Ratio
Expresses the relationship between the return (payoff) and the risk (standard deviation).
RRR = Return to Risk Ratio =
RRRSoft Drinks = 125/75 = RRRHot Dogs = 9
You might wish to choose Hot Dogs. Although Soft Drinks have the higher Expected Monetary Value, Hot Dogs have a much larger return to risk ratio and a much smaller CV.
Note: RRR is the inverse of CV