19.1 Payoff Tables and Decision Trees

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USING STATISTICS @ The Reliable Fund As the manager of The Reliable Fund, you are responsible for purchasing and selling stocks for the fund. The investors in this mutual fund expect a large return on their investment, and at the same time they want to minimize their risk. At the present time, you need to decide between two stocks to purchase. An economist for your company has evaluated the potential one-year returns for both stocks, under four economic conditions: recession, stability, moderate growth, and boom. She has also estimated the probability of each economic condition occurring. How can you use the information provided by the economist to determine which stock to choose in order to maximize return and minimize risk? 3
4 CHAPTER 19 Decision Making EXAMPLE 19.1 A Payoff Table for Deciding How to Market Organic Salad Dressings In Chapter 4, you studied various rules of probability and used Bayes’ theorem to revise probabilities. In Chapter 5, you learned about discrete probability distributions and how to compute the expected value. In this chapter, these probability rules and probability distributions are applied to a decision-making process for evaluating alternative courses of action. In this context, you can consider the four basic features of a decision-making situation: • Alternative courses of action A decision maker must have two or more possible choices to evaluate prior to selecting one course of action from among the alternative courses of action. For example, as a manager of a mutual fund in the Using Statistics scenario, you must decide whether to purchase stock A or stock B. • Events A decision maker must list the events, or states of the world that can occur and consider the probability of occurrence of each event. To aid in selecting which stock to purchase in the Using Statistics scenario, an economist for your company has listed four possible economic conditions and the probability of occurrence of each event in the next year. • Payoffs In order to evaluate each course of action, a decision maker must associate a value or payoff with the result of each event. In business applications, this payoff is usually expressed in terms of profits or costs, although other payoffs, such as units of satisfaction or utility, are sometimes considered. In the Using Statistics scenario, the payoff is the return on investment. • Decision criteria A decision maker must determine how to select the best course of action. Section 19.2 discusses five decision criteria: maximax payoff, maximin payoff, expected monetary value, expected opportunity loss, and return-to-risk ratio. 19.1 Payoff Tables and Decision Trees TABLE 19.1 Payoff Table for the Organic Salad Dressings Marketing Example (in Millions of Dollars) In order to evaluate the alternative courses of action for a complete set of events, you need to develop a payoff table or construct a decision tree. A payoff table contains each possible event that can occur for each alternative course of action and a value or payoff for each combination of an event and course of action. Example 19.1 discusses a payoff table for a marketing manager trying to decide how to market organic salad dressings. You are a marketing manager for a food products company, considering the introduction of a new brand of organic salad dressings. You need to develop a marketing plan for the salad dressings in which you must decide whether you will have a gradual introduction of the salad dressings (with only a few different salad dressings introduced to the market) or a concentrated introduction of the salad dressings (in which a full line of salad dressings will be introduced to the market). You estimate that if there is a low demand for the salad dressings, your first year’s profit will be $1 million for a gradual introduction and - $5 million (a loss of $5 million) for a concentrated introduction. If there is high demand, you estimate that your first year’s profit will be $4 million for a gradual introduction and $10 million for a concentrated introduction. Construct a payoff table for these two alternative courses of action. SOLUTION Table 19.1 is a payoff table for the organic salad dressings marketing example. ALTERNATIVE COURSE OF ACTION EVENT, E i Gradual, A 1 Concentrated, A 2 Low demand, E 1 1 -5 High demand, E 2 4 10 Using a decision tree is another way of representing the events for each alternative course of action. A decision tree pictorially represents the events and courses of action through a set of branches and nodes. Example 19.2 illustrates a decision tree.
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19.1 Payoff Tables and Decision Trees

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