# Analyzing Business Problems Using Decision Trees & Payoff Tables

Lesson Transcript
Instructor: Natalie Boyd

Natalie is a teacher and holds an MA in English Education and is in progress on her PhD in psychology.

Decision trees and payoff tables can be used to help in analyzing business problems. In this lesson, review some business decisions that are often made, then look at decision trees and payoff tables. Updated: 11/09/2021

Chloe has a big decision to make. Her business is doing pretty well, and she thinks it might be time to expand. But to do that, she needs to take on a business loan. If the expansion is a good decision, that loan will pay off. But if it's not a good decision, it could bankrupt her business. What should she do?

Business owners face decisions every day, from whether or not to expand, what materials to use, how their logo and website should look, and even what pens and pencils to stock in the office! So, how can someone like Chloe make the right choices? There are several ways to make decisions. Often, the first thing that happens is that a business owner analyzes different possible paths. To do that, many employ decision trees or payoff tables. To help Chloe out in her decision-making process, let's look at both options.

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## Decision Trees

Chloe needs to figure out whether or not to take out a loan and expand her business. But it's a complicated decision, and there are a lot of things that can cause it to be a good or bad decision in the long run. One way to analyze the possible outcome of a decision is to make a decision tree, which is a diagram representing all possible outcomes of a solution. It's called a decision tree because once the diagram is finished, it kind of looks like a tree.

There are several major elements to a diagram tree. The first are little squares. These represent decision alternatives, or choices that a business can make. For example, the first square in Chloe's decision tree will likely represent the choice of whether or not to take out a loan and expand.

Each decision square has two or more lines diverging from it. These are like the paths that Chloe can take. If she chooses yes to expansion, she'll go down one path. If she chooses no to expansion, she'll go down another.

Of course, each decision path leads to another decision. For example, if she chooses to expand, then she's left with decisions like how big of a loan to take out and which departments to invest in first. Each time she makes a decision, more paths (or branches on the tree) emerge from the square representing that decision.

But squares and branches aren't the only thing on Chloe's tree. Remember that there are some things that can influence whether a decision ends up being a good one or a bad one. Some of these are out of her control. For example, what if she chooses to expand, and then the economy tanks and she loses customers? Future events that are not under the control of the business are called states of nature and are represented on a decision tree by circles. They, too, lie along a branch and have multiple branches flowing from them.

Let's go back to Chloe's decision tree for a minute. She first decides that yes, she wants to take out a loan and expand. That takes her to her next decision: how big should her loan be? Her choices are \$1 million, \$500,000, or \$300,000. Each of those choices have branches going out from them.

At this point, she's faced with a state of nature: the possibility of the economy tanking. For the state of nature of 'economy tanking,' there are a few possibilities: it can stay strong, there can be a small recession, or a huge depression. If she takes out a \$1 million loan and the economy crashes, she's in a bad place. But, if she takes out a \$300,000 loan and things go south, she's not as vulnerable. But for each loan value, she'll have to analyze the outcomes of the three possibilities of the economy crashing.

Chloe will want to continue creating branches (or paths) and adding in decision alternatives and states of nature until she runs out of possibilities. Then, she can go back through her decision tree and try to figure out which outcomes are most likely and also compare the worst- and best-case scenarios.

## Payoff Tables

A decision tree seems like it can help Chloe make an informed decision, but it also seems a little overwhelming to her. All those decision alternatives and states of nature make her decision tree very big and scary looking! Is there another way?

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