52. Decision Analysis
Alternatives and States of Nature
Good Decisions vs. Good Outcomes
Payoff Matrix
Decision Trees
Utility Functions
Decisions under Uncertainty
Decisions under Risk

53. Decision Analysis - Payoff Tables
Case Problem - (A) p. 38

54. Decision Analysis - Payoff Tables

55. Decision Analysis - Payoff Tables

56. Decision Analysis - Payoff Tables
Decisions under Uncertainty

57. Decision Analysis - Payoff Tables
Decisions under Uncertainty

58. Decision Analysis - Payoff Tables
Decisions under Uncertainty

59. Decision Analysis - Payoff Tables
Decisions under Risk

60. Decision Analysis - Payoff Tables
Decisions under Risk

61. Decision Analysis - Payoff Tables
Decisions under Risk

62. 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.

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

64. 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.

65. 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.

66. 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).

67. 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.

68. 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 Then the utility that
the decision maker assigns to the $450 is
0.7.

69. Decision Analysis - Utility Theory Constructing Utility Functions

70. Decision Analysis - Utility Theory Constructing Utility Functions

71. 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

72. Decision Analysis - Utility Theory The Exponential Utility Function