Good Decisions vs Good Outcomes Payoff Matrix Decision Trees Utility Functions Decisions under Uncertainty Decisions under Risk Decision Analysis Payoff Tables Case Problem A p 38 Decision Analysis Payoff Tables ID: 1028158
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1. Decision AnalysisAlternatives and States of NatureGood Decisions vs. Good OutcomesPayoff MatrixDecision TreesUtility FunctionsDecisions under UncertaintyDecisions under Risk
2. Decision Analysis - Payoff TablesCase Problem - (A) p. 38
3. Decision Analysis - Payoff Tables
4. Decision Analysis - Payoff Tables
5. Decision Analysis - Payoff TablesDecisions under Uncertainty
6. Decision Analysis - Payoff TablesDecisions under Uncertainty
7. Decision Analysis - Payoff TablesDecisions under Uncertainty
8. Decision Analysis - Payoff TablesDecisions under Risk
9. Decision Analysis - Payoff TablesDecisions under Risk
10. Decision Analysis - Payoff TablesDecisions under Risk
11. Decision Analysis - Utility TheoryUtility theory provides a way to incorporate the decision maker’s attitudes and preferences toward risk and return in the decision analysis process so that the most desirable decision alternative is identified.A utility function translates each of the possible payoffs in a decision problem into a non-monetary measure known as a utility.
12. Decision Analysis - Utility TheoryUtilityPayoff1.000.750.500.250risk seekingrisk neutralrisk averse
13. Decision Analysis - Utility TheoryThe utility of a payoff represents the total worth, value, or desirability of the outcome of a decision alternative to the decision maker.A risk averse decision maker assigns the largest relative utility to any payoff but has a diminishing marginal utility for increased payoffs.
14. Decision Analysis - Utility TheoryA risk seeking decision maker assigns the smallest utility to any payoff but has an increasing marginal utility for increased payoffs.A risk neutral decision maker falls in between these two extremes and has a constant marginal utility for increased payoffs.
15. Decision Analysis - Utility TheoryConstructing Utility FunctionsStep 1 - Assign a utility value of 0 to the worst outcome (W) in a decision problem and a utility value of 1 to the best outcome (B).
16. Decision Analysis - Utility TheoryConstructing Utility FunctionsStep 2 - For any other outcome x, find the probability p at which the decision maker is indifferent between the following two alternatives:Receive x with certainty orReceive B with probability p or W with probability 1-p The value of p is the utility that the decision maker assigns to the outcome x.
17. Decision Analysis - Utility TheoryConstructing Utility FunctionsReceive $450 with certaintyPlay a game in which the decision maker can make $5,800 with probability p or lose $2,360 with probability 1-p Let’s assume that the value of p that makes these two choices equally attractive to the decision maker is 0.7. Then the utility that the decision maker assigns to the $450 is 0.7.For example, let’s compute the utility forthe $450 entry that corresponds to alternativeA and state of nature N=30. The problemconsists on finding the value of p that makesthe following two options equally attractive for the decision maker:
18. Decision Analysis - Utility TheoryConstructing Utility Functions
19. Decision Analysis - Utility TheoryConstructing Utility Functions
20. Decision Analysis - Utility TheoryThe Exponential Utility FunctionA sensible value for R is the maximum value of Y for which the decision maker is willing to participate in a game of chance with the following possible outcomes:Win $Y with probability 0.5Lose $Y/2 with probability 0.5
21. Decision Analysis - Utility TheoryThe Exponential Utility Function