Decision Theory

Chapter 11Decision TheoryPart 3 Probabilistic Decision ModelsLearning ObjectivesOutline the characteristics of a decision theory approach to decision making.Describe and give examples of decisions under certainty, risk, and complete uncertainty.Make decisions using maximin, maximax, minimax regret, Hurwicz, equally likely, and expected value criteria and use Excel to solve problems involving these techniques.Use Excel to solve decision-making problems under risk using the expected value criterion.After completing this chapter, you should be able to:2Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Learning Objectives (cont’d)Develop decision trees that consist of a combination of decision alternatives and events.Use TreePlan to develop decision trees with Excel.Determine if acquiring additional information in a decision problem will be worth the cost.Calculate revised probabilities manually and with Excel.Analyze the sensitivity of decisions to probability estimates.Describe how utilities can be used in lieu of monetary value in making decisions.After completing this chapter, you should be able to:3Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Decision TheoryDecision theory problems are characterized by the following:A list of alternatives.A list of possible future states of nature.Payoffs associated with each alternative/state of nature combination.An assessment of the degree of certainty of possible future events.A decision criterion.4Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 11-1Suppose that a real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has ruled out “do nothing” and is left with the following list of acceptable alternatives: 1. Residential proposal. 2. Commercial proposal #1. 3. Commercial proposal #2.Suppose that the developer views the possibilities as 1. No shopping center. 2. Medium-sized shopping center. 3. Large shopping center.5Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–1 General Format of a Decision Table6Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–2 Payoff Table for Real Estate Developer7Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–3 If It Is Known That No Shopping Center Will be Built, Only the First Column Payoffs Would Be RelevantDecision Making under Certainty8Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Decision Making under Complete UncertaintyApproaches to decision making under complete uncertainty:MaximinMaximax.Minimax regret.HurwiczEqual likelihood9Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–4 Maximin Solution for Real Estate ProblemMaximinThe maximin strategy is a conservative one; it consists of identifying the worst (minimum) payoff for each alternative and then selecting the alternative that has the best (maximum) of the worst payoffs. In effect, the decision maker is setting a floor for the potential payoff; the actual payoff cannot be less than this amount.10Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–5 Maximax Solution for Real Estate ProblemMaximaxThe maximax approach is the opposite of the previous one: The best payoff for each alternative is identified, and the alternative with the maximum of these is the designated decision.11Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–6 Payoff Table with Similar Maximum PayoffsMinimax RegretAn approach that takes all payoffs into account. To use this approach, it is necessary to develop an opportunity loss table that reflects the difference between each payoff and the best possible payoff in a column (i.e., given a state of nature). Hence, opportunity loss amounts are found by identifying the best payoff in a column and then subtracting each of the other values in the column from that payoff.12Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–7 Opportunity Loss Table for Real Estate Problem13Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–8 Identifying the Minimax Regret Alternative14Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–9 Minimax Regret Can Lead in a Poor Decision15Copyright © 2007 The McGraw-Hill Companies. All rights reserved. The Hurwicz (Realism) Criterion (Weighted Average or Realism Criterion)The approach offers the decision maker a compromise between the maximax and the maximin criteria. Requires the decision maker to specify a degree of optimism, in the form of a coefficient of optimism α, with possible values of α ranging from 0 to 1.00. The closer the selected value of α is to 1.00, the more optimistic the decision maker is, and the closer the value of α is to 0, the more pessimistic the decision maker is.16Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–10 Equal Likelihood Criterion17Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–11 Summary of Methods for Decision Making under Complete Uncertainty18Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11-1 Using Excel to Make Decisions under Complete Uncertainty19Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Decision Making under RiskDecision making under partial uncertaintyDistinguished by the present of probabilities for the occurrence of the various states of nature under partial uncertainty. The term risk is often used in conjunction with partial uncertainty.Sources of probabilitiesSubjective estimatesExpert opinionsHistorical frequencies20Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–12 Real Estate Payoff Table with ProbabilitiesExpected Monetary Value (EMV) approachProvides the decision maker with a value that represents an average payoff for each alternative. The best alternative is, then, the one that has the highest expected monetary value. The average or expected payoff of each alternative is a weighted average: the state of nature probabilities are used to weight the respective payoffs. 21Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Approaches to Incorporating Probabilities in the Decision Making ProcessExpected Monetary Value (EMV) approachProvides the decision maker with a value that represents an average payoff for each alternative.Expected Opportunity Loss (EOL)The opportunity losses for each alternative are weighted by the probabilities of their respective states of nature to compute a long-run average opportunity loss, and the alternative with the smallest expected loss is selected as the best choice.Expected Value of Perfect Information (EVPI)A measure of the difference between the certain payoff that could be realized under a condition of certainty and the expected payoff under a condition involving risk.22Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11-2 Using Excel to Make Decisions under Risk23Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–1 Decision Tree FormatDecision trees are used by decision makers to obtain a visual portrayal of decision alternatives and their possible consequences. 24Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–2 Decision Tree for Real Estate Developer Problem25Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–3 Real Estate Problem with a Second Possible Decision26Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–3 Initial TreePlan Dialog Box27Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–4 Decision Tree Initially Developed by TreePlan28Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–5 TreePlan Dialog Box to Add Branches, Decision Nodes,or Events29Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–6 Modified Decision Tree with Three Branches30Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–7 TreePlan Dialog Box to Add or Change Decision Nodesor Events31Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–8 Modified Decision Tree with Three Branches and the Added Event Node with Three Nodes32Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–9 Excel Solution to the Real Estate Developer Decision Tree Problem33Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–4 Sequential Decision Tree for Unicom Inc. (Example 11-3, part a)34Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–10 Excel Solution to the Unicom Inc. Sequential Decision Tree Problem35Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–5 Conceptual Portrayal of Market Test Example36Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Test Market Payoffs37Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–6 Summary of Analysis of Market Test Example38Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–13 Reliability of Market Test39Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–14 Probability Calculations Given the Market Test Indicates a Strong Market40Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 11–15 Probability Calculations Given the Market Test Indicates aWeak MarketConditional probabilities express the reliability of the sampling device (e.g., market test) given the condition of actual market type.41Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–11 Calculation of the Revised Probabilities for the Market Test Example42Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–7 Format of Graph for Sensitivity AnalysisSensitivity Analysis enables decision makers to identify a range of probabilities over which a particular alternative would be optimal.43Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–8 The Expected Value Line for Alternative a.44Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–9 Example of Finding the Expected Value for Alternative a when P(#2) Is .5045Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–10 All Three Alternatives Are Plotted on a Single Graph46Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–11 The Line with the Highest Expected Profit Is Optimal for a Given Value of P(#2)47Copyright © 2007 The McGraw-Hill Companies. All rights reserved. UtilityUtility (of a payoff)A measure of the personal satisfaction associated with a payoff.RiskA decision problem in which the states of nature have probabilities associated with their occurrence.Risk AvertersIndividuals that avoid taking risks. The decision maker has less utility for greater risk.Risk TakersIndividuals that like taking risks and that have a greater utility for the potential winnings even though their chances of winning are very low.48Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 11–12 Converting P(#2) Ranges into P(#1) Ranges49Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–12 Solved Problem 1: Decision Making under Complete Uncertainty—A Profit Maximization Problem (Part f)50Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–13 Solved Problem 2: Decision Making under Complete Uncertainty—A Cost Minimization Problem (part f)51Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–14 Calculation of the Revised Probabilities and Expected Value of Perfect Information for Solved Problem 3 (part c)52Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–15 Calculation of the Revised Probabilities for Solved Problem 5(part c)53Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–16 TreePlan Dialog Box to Add Branches, Decision Nodes, or EventsExhibit 11–17 TreePlan Dialog Box to Add or Change Decision Nodes or Events54Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 11–18 Decision Tree for Solved Problem 5 (part c)55Copyright © 2007 The McGraw-Hill Companies. All rights reserved.