# Chapter Topics The Payoff Table and Decision Trees Opportunity Loss

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Chapter Topics The Payoff Table and Decision Trees Opportunity Loss

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)

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

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

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

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

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

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

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

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

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

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

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)

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.

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%

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

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