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
Decision Analysis - Payoff Tables Decisions under Uncertainty
Decision Analysis - Payoff Tables Decisions under Uncertainty
Decision Analysis - Payoff Tables Decisions under Uncertainty
Decision Analysis - Payoff Tables Decisions under Risk
Decision Analysis - Payoff Tables Decisions under Risk
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 risk averse 1.00 risk neutral 0.75 risk seeking 0.50 0.25 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 Theory Constructing 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 Theory Constructing 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 Theory Constructing 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 Theory Constructing Utility Functions
Decision Analysis - Utility Theory Constructing Utility Functions
Decision Analysis - Utility Theory The 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 Theory The Exponential Utility Function