Decision Analysis

Decision Analysis • Alternatives and States of Nature • 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

Decision Analysis - Payoff Tables Decisions under Uncertainty

Decision Analysis - Payoff Tables Decisions under Risk

Decision Analysis - Utility Theory • Utility 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.

Decision Analysis - Utility Theory Utility risk averse 1.00 risk neutral 0.75 risk seeking 0.50 0.25 0 Payoff

Decision Analysis - Utility Theory • The 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.

Decision Analysis - Utility Theory • A 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.

Decision Analysis - Utility TheoryConstructing Utility Functions • Step 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).

Decision Analysis - Utility TheoryConstructing Utility Functions • Step 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 or • Receive 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.

Decision Analysis - Utility TheoryConstructing Utility Functions For example, let’s compute the utility for the $450 entry that corresponds to alternative A and state of nature N=30. The problem consists on finding the value of p that makes the following two options equally attractive for the decision maker: • Receive $450 with certainty • Play 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.

Decision Analysis - Utility TheoryConstructing Utility Functions

Decision Analysis - Utility TheoryThe Exponential Utility Function • A 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 0.5 • Lose $Y/2 with probability 0.5

Decision Analysis - Utility TheoryThe Exponential Utility Function

Decision Analysis