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**Introduction to Decision Analysis**

CD-ROM Chapter 17 Introduction to Decision Analysis

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**Chapter 17 - Chapter Outcomes**

After studying the material in this chapter, you should be able to: Describe the decision-making environments of certainty and uncertainty. Construct both a payoff table and an opportunity loss table. Define the expected value criterion. Apply the expected value criterion in decision situations. Compute the value of perfect information.

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**Chapter 17 - Chapter Outcomes (continued)**

After studying the material in this chapter, you should be able to: Develop a decision tree and explain how it can aid decision making in an uncertain environment. Discuss the difference between risk seeking and risk avoiding behavior. Construct an individual risk preference function.

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**Decision-Making Environments**

Certainty refers to a decision environment in which the results of selecting each alternative are known before the decision is made.

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**Decision-Making Environments**

Uncertainty refers to a decision environment in which the decision maker does not know what outcome will occur when an alternative is selected.

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**Decision-Making Environments**

The goal of decision analysis is to focus on making good decisions, which in the long run should result in an increased number of good outcomes.

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Decision Criteria The states of nature are the possible outcomes in a decision situation over which the decision maker has no control.

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Decision Criteria A payoff is the outcome (profit or loss) for any combination of alternative states of nature. The outcomes of all possible combinations of alternatives and states of nature constitute a payoff table.

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**Decision Criteria (Table 17-2)**

DEMAND (STATES OF NATURE) Alternative S 1 Large Increase 2 Moderate Increase 3 Small Increase A Large Investment $6,000,000 $4,000,000 $-2,600,000 Medium Investment 2,500,000 5,000,000 -1,000,000 Small Investment 2,000,000 1,500,000 1,200,000 Fisher Fabrication Payoff Table

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Decision Criteria The maximax criterion is an optimistic decision criterion for dealing with uncertainty without using probability. For each option, the decision maker finds the maximum possible payoff and then selects the option with the greatest maximum payoff.

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Decision Criteria The maximin criterion is a pessimistic (conservative) decision criterion for dealing with uncertainty without using probability. For each option, the decision maker finds the minimum possible payoff and then selects the option with the greatest minimum payoff.

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Decision Criteria The opportunity loss is the difference between the actual payoff that occurs for a decision and the optimal payoff for the same decision.

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Decision Criteria The minimax regret criterion is a decision criterion that considers the costs of selecting the “wrong” alternative. For each sate of nature, the decision maker finds the difference between the best payoff and each other alternative and uses these values to construct an opportunity-loss table. The decision maker then selects the alternative with the minimum opportunity loss (or regret).

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**Decision Criteria (Table 17-3)**

Fisher Fabrication Opportunity-Loss Table

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**Decision Criteria (Table 17-4)**

Fisher Fabrication Maximum Regret Table

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Decision Criteria The expected-value criterion is a decision criterion that employs probability to select the alternative that will produce the greatest average payoff or minimum average loss.

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**Decision Criteria EXPECTED VALUE where:**

xi = The ith outcome of the specified alternative measured in some units, such as dollars P(xi) = The probability of outcome xi occurring k = number of potential outcomes and:

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**CLASSICAL PROBABILITY ASSESSMENT**

Decision Criteria CLASSICAL PROBABILITY ASSESSMENT

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**RELATIVE FREQUENCY OF OCCURRENCE PROBABILITY where:**

Decision Criteria RELATIVE FREQUENCY OF OCCURRENCE PROBABILITY where:

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**Decision Criteria (Table 17-5)**

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**Decision Criteria (Table 17-6)**

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**Decision-Tree Analysis**

A decision tree is a diagram that illustrates the correct ordering of actions and events in a decision-analysis problem. Each act or event is represented by a node on the decision tree.

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**Decision-Tree Analysis (Figure 17-1)**

Don’t sign Sign Contract Decision

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**Decision-Tree Analysis (Figure 17-2)**

Don’t sign Unfavorable Review Sign Contract Favorable Review Decision Event

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**Decision-Tree Analysis (Figure 17-3)**

Don’t sign Unfavorable Review Hardcover Sign Contract Favorable Review Decision Paperback Event Decision

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**Decision-Tree Analysis (Figure 17-4)**

Don’t sign Unfavorable Review 100,000 copies Hardcover Sign Contract 1,000,000 copies Favorable Review 50,000 copies Decision Paperback Event 1,500,000 copies Decision Event

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**Risk Preference Attitudes**

A risk-neutral attitude refers to the preference for risk under which the alternative with the highest expected payoff or lowest expected cost will be selected.

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**Risk Preference Attitudes (Figure 17-11)**

Merger $10 (0.5) Buy (0.5) -$5 No Merger $0 Don’t Buy Xircom Stock Purchase Example

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**Risk Preference Attitudes (Figure 17-12)**

Merger $100 (0.5) Buy (0.5) -$50 No Merger $0 Don’t Buy Xircom Stock Purchase Example

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**Risk Preference Attitudes (Figure 17-13)**

Merger $10,000 (0.5) Buy (0.5) -$5,000 No Merger $0 Don’t Buy Xircom Stock Purchase Example

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**Risk Preference Attitudes**

A risk-averse attitude refers to the preference for risk such that the decision maker could select an alternative with a lower expected payoff in order to avoid the possibility of an undesirable outcome.

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**Risk Preference Attitudes**

Certainty equivalent is the value that would make a decision maker indifferent between taking an uncertain gamble versus receiving that value instead of taking the gamble.

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**Risk Preference Attitudes**

A risk-seeking attitude refers to the preference for risk such that the decision maker could select an alternative with a lower expected payoff in hopes of achieving an outcome with a more desirable result.

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**Risk Preference Attitudes**

The risk preference function is the graph that describes a decision maker’s preference for risk over the range of possible payoffs.

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**Risk Preference Attitudes**

A standard gamble approach is the approach for assessing risk-preference functions that involves setting up a series of gambles between two payoffs and determining the certainty equivalent for each gamble.

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**Risk Preference Attitudes**

A preference quotient refers to the measure of the relative utility for the outcomes of a decision on a scale between 0.0 and 1.0.

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**Risk Preference Attitudes (Figure 17-16)**

End Values q Values $10,000 1.0 0.5 Play 0.5 -$2,000 0.0 CE = ? Don’t Play Assessing the Risk-Preference Function: Standard Gamble 1

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**Risk Preference Attitudes (Figure 17-17)**

End Values q Values $10,000 1.0 0.5 Play 0.5 $4,000 0.5 CE = ? Don’t Play Assessing the Risk-Preference Function: Standard Gamble 2

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**Risk Preference Attitudes (Figure 17-18)**

End Values q Values $4,000 0.5 0.5 Play 0.5 -$2,000 0.0 CE = ? Don’t Play Assessing the Risk-Preference Function: Standard Gamble 3

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**Risk Preference Attitudes**

Risk premium is the difference between the expected value of an event and the certainty equivalent. The risk premium will be zero for a risk-neutral decision maker, positive for a risk-averse decision maker, and negative for a risk-seeking decision maker.

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**Risk Preference Attitudes (Figure 17-19)**

0.75 0.50 0.25 -$2,000 $0 $2,000 $4,000 $6,000 $8,000 $10,000 Risk-Neutral Preference Function

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**Risk Preference Attitudes (Figure 17-23)**

0.75 0.50 0.25 -$2,000 $0 $2,000 $4,000 $6,000 $8,000 $10,000 Risk-Averse Preference Function

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**Risk Preference Attitudes (Figure 17-26)**

0.75 0.50 0.25 -$2,000 $0 $2,000 $4,000 $6,000 $8,000 $10,000 Risk-Seeking Preference Function

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**Key Terms • Certainty • Certainty Equivalent • Decision Tree**

• Expected Value • Expected-Value Criterion • Maximax Criterion • Maximin Criterion • Minimax Regret Criterion • Opportunity Loss • Payoff • Preference Quotient • Risk-Averse Attitude • Risk-Neutral Attitude • Risk-Preference Function • Risk Premium • Risk-Seeking Attitude

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**Key Terms (continued) • Standard Gamble Approach • State of Nature**

• Uncertainty

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Decision Theory Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill.

Decision Theory Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill.

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