## Decision Sciences 433

### Course title: Decisions and Risk

Course catalog description: The course introduces fundamental concepts and methods for decision analysis under uncertainty. The first part of the course provides basic concepts and methods of probability including elementary laws of probability and conditional probability, discrete and continuous random variables, their probability distributions, means and standard deviations, and joint distributions of portfolios of random variables. The second part of the course deals with decision making under uncertainty, and the value of information. The final part of the course focuses on sampling distributions and point and interval estimation of means and proportions of populations. Throughout the course, computer simulation models and spreadsheets are used to facilitate business analyses.

### Course Overview

In the first part of this course we'll be covering four major topics: “The Language of Probability,” “Random Variables,” “Commonly-Encountered Probability Distributions,” and “Decision Trees.” We'll follow up with an “Introduction to Statistics” (covering the language of estimation), with brief forays into “Game Theory” and “Simulation.” Throughout the course we'll explore the use of modern spreadsheet tools to aid in decision analysis.

The reason this course comes at the beginning of every management program is simple: Whether your primary area of interest is marketing, finance, operations, accounting, human resource management, or some extension or combination of these, you constantly face the need to make decisions in the face of uncertainty. All of the courses that follow this one will use a single common language to discuss risk and uncertainty ... and our objective over the next quarter will be to become comfortable speaking that language.

You all probably remember the first time you studied a language other than that you learned as an infant. Your first “foreign” language course talked about grammar, rules of speech, verb declensions, and the like. But the goal of the course was to reach the point where you didn't need to focus on the rules, but could simply think and speak (and do business) in the new language. We'll be taking a similar approach here: Don't lose sight of our objective. While we'll spend much of the early time on rules and definitions, our ultimate goal is to learn to think and speak clearly when using the language of probability to address management issues.

Your professors in all of your subsequent Kellogg courses will assume that you are comfortable with all of the material listed here.

### Dealing with Uncertainty

If we lived in a world of certainty, being a manager would be the easiest job in that world. Whenever a decision had to be made, we would simply consider each choice available to us and predict the consequences of that choice, and then implement whichever choice led to the most desirable predicted outcome[1].

Unfortunately, the world isn't so simple. (Or, perhaps it is fortunate that the world is somewhat more complex, since otherwise managers wouldn't be paid so much!) Two types of uncertainty complicate the job of a manager.

The first is called “randomness” - The outcome of a choice we make might depend on things we can't directly observe or control. Imagine that you're planning a party, and must decide how much (and what types of) food to order. Even if you know how many people you've invited, you still face uncertainties concerning how many guests actually show up, how hungry they will be, and what their food preferences are. You can't perfectly predict the outcome of your ordering decision.

Similarly, a petroleum company, trying to decide whether to drill on a tract of land, doesn't know whether there's an underground oil reservoir under the tract, and, even if there is, doesn't know precisely where it is, or how large it is.

In this drilling example, note that “Nature” has already - millions of years ago[2] - determined the location and size of the oil reserves. Philosophers have argued for centuries over whether it's appropriate to call such things “random,” since they are actually already determinate (known to God, if you will). In all of our discussions, we'll take the view that randomness is subjective: It is in the eyes of the beholder. God might know if there's oil there. So might a competitor who has already drilled an offset well from a neighboring tract of land. But, if we don't yet have specific knowledge, then - to us - the location and quantity are indeed (subjectively) random.

The language, and tools, of probability provide us with a way to analyze decisions in the face of randomness. This is what the first core “decision analysis” class at Kellogg (DECS-433,-436,-438A) has as its primary focus.

The randomness we'll be studying will, predominantly, be the consequence of actions taken by “Nature,” a neutral actor with no self-interest. There is another type of randomness, which arises from our uncertainty concerning the actions of other self-motivated decision-makers. This type of randomness is the focus of game theory, which we will discuss briefly in this course (and which is discussed in more detail in subsequent courses, particularly DECS-452). For example, if we were to analyze a two-person poker game, questions concerning the likelihood of hands of various strengths being dealt to one party or the other are pure “probability” questions. Issues involving how to bet, or how to interpret the betting behavior of a competitor, lie in the realm of “game theory.”

The other type of uncertainty that a manager faces is uncertainty concerning the precise nature of the relationships between actions and their consequences. A brand manager might “know” that demand for a product will be lower at higher prices, but not know the specific relationship between price and demand. This makes it impossible to predict the outcome of a pricing decision.

The field of statistics provides a tool - regression analysis - that can help us estimate the nature of the relationships we face, on the basis of relevant sample data. The second core “decision analysis” course at Kellogg (DECS-434,-437,-439B) develops and applies this tool.

To summarize, consider the proprietor of a specialty shop deciding how to price umbrellas. Ultimately, the ideal price will depend on local weather and the needs of individual customers (some of whom may have recently lost their umbrellas, or had them break), as well as on the pricing decisions made by other umbrella shops in the area. To make the best pricing decision, the proprietor must deal with probability issues (concerning the weather and consumer needs), game theory issues (concerning how other shops might price their products, or respond to his pricing decision), and statistical issues (concerning how the number of purchasers buying his umbrellas is influenced by the weather, and by his and his competitors' pricing decisions). In order to make an appropriate decision, a manager must be prepared to deal with all of these types of uncertainty.

[1] God forbid that I use the first paragraph of this section to sweep under the rug two important issues: Managers, in that certain world, would still face two challenges: Determining what “desirable” means, and finding the best policy when there are so many choices available that they can't simply be listed and evaluated one-by-one. We'll discuss these issues, as well, during the course.

[2] A recent Gallup poll asked adult Americans how they believed the human race originated. 46% of the respondents (other polls show they're mostly Republicans) chose "God created human beings pretty much in their present form at one time within the last 10,000 years or so," the statement that most closely describes biblical creationism. If you don't believe that the Earth is more than 10,000 years old, make up your own example here.