## What is Decision Theory?

Decision theory, also known as the theory of choice, is a branch of statistics that deals with making decisions based on the probability of the occurrence of an event. The chief purpose of decision theory is to identify the best course of action for the company with maximum payoffs.

## Components of Decision Theory

The Decision Theory consists of:

**Decision Maker**

The decision-maker is the person entitled to make the decisions on behalf of the company. The decision theory starts with the decision-maker when the identification of all the possibilities is done and subsequently, the outcomes such as profits, costs, and margins are calculated. After evaluation and identification, optimum decisions are taken, which maximize the productivity of the business. Optimum decisions involve maximizing profit, revenue, and margins and minimizing expenses such as cost, inefficiencies, and time.**The course of action**

A course of action comprises a series of steps and acts taken, which lead to an outcome. These acts are evaluated in decision theory and the decision-maker analyzes the best course of action to achieve the goals of reaching optimal decisions.**Outcomes**

Outcomes are the result of the actions for each decision. These are the results that will be achieved when a particular course of action is taken into consideration.**Payoffs**

Payoffs are the returns on the outcome for a given decision. For instance, while selecting and evaluating a supplier, if X Inc. is providing the raw material at $8 per unit and Y Inc. provides the same at $8.5, choosing X Inc. over Y Inc. will save 50 cents on every unit purchased. The saving of 50 cents per purchase of each unit is considered to be the payoff.

## Types of Decisions

Decisions are affected by the externalities. Below are the different types of decision theories based on different external situations:

### Under certainty

Under certainty, the decision-maker with a larger degree of certainty knows all the courses of action, the outcomes of those actions, and the payoffs which will be generated by following a certain course of action. The outcomes can easily be known beforehand and decisions can be based on those outcomes. Generally, these conditions occur when opting for decisions that the decision-maker has taken earlier and has experience in. The outcomes are quantifiable, comparable, static, and predictable.

### Under risk

When any of the information regarding the decision-making is not present and the situation is unknown, an element of risk arises while taking any decision. Under risk, the outcome for every action is available but information about every alternative action plan is known in the form of probability which is to be observed and analyzed to reach optimum decisions.

### Under conflict

Under conflict, the actions that are pursued can be impacted. In modern times, brands compete with one another rigorously and the course of action of the competition can affect the outcome of the competing brand. For instance, PepsiCo chooses a particular potato supplier for its potato chips, which affects the decision-making of other potato chip makers. Under conflict, decisions are taken considering the actions, and actions are taken considering counteractions by the opponent.

## Calculation of Decision Theory

Let us solve a problem for further clarity on decision theory

Course of Action | s_{1} | s_{2} | s_{3} | Maximum | Minimum | Average |

a_{1} | 130 | 0 | 90 | 130 | 0 | 73.33 |

a_{2} | 0 | 110 | 120 | 120 | 0 | 76.67 |

a_{3} | 152 | -30 | 160 | 160 | -30 | 94.00 |

a_{4} | 69 | 44 | 22 | 69 | 22 | 45.00 |

In the above table, a_{1}, a_{2}, a_{3}, and a_{4} are the courses of action while s_{1}, s_{2}, and s_{3} are the states. The table denotes decision theory under certainty where you can see the outcome of each action and state are predetermined.

Under Maximin principles of decision theory, the minimum number is taken from the actions i.e. (0, 0, -30, 22) and the maximum out of this minimum is selected. In this case, the maximum in this minimum is 22 thus maximin is 22 which is a_{4}. A maximin is a conservative approach taken in decision theory to predict the outcome to make sure that management at least delivers the promised results. It makes sure that what is promised is delivered.

According to Maximax criteria, the maximum number is taken from the actions i.e. (130, 120, 160, 69) and the maximum out of this maximum is selected. In this case, the maximum is 160 thus maximax is 160 which is a_{3}. The maximax is used while formulating what could be the maximum output derived while following a course of action.

According to Minimin criteria, the minimum number is taken from the actions i.e. (0, 0, -30, 22) and the minimum is selected. In this case, the minimum is -30, which is a_{3}. This approach is the worst-case scenario that can come out of these actions.

According to Laplace criteria, the maximum number is taken from the average of the actions i.e (73.33, 76.67, 94, 45) and the maximum out of these averages is selected. In this case, the maximum is 76.67 thus Laplace is 76.67. which is a_{2}.

## Context and Applications

This subject is important in professional exams for both undergraduate and graduate levels, particularly in statistics, probability, and management studies. . It is a branch of applied probability theory. The courses covering decision theory are business management, Organizational management, etc.

## Practice Problems

**Q1. **Which of the following is not a component of decision-making?

- Course of action
- Outcomes
- Payoffs
- Probability

Correct Answer**:** Option d.

Explanation: Probability of choice is a very useful tool to select and analyze the right course of action that is taken by the company. It is a tool to evaluate the path of actions and not a component of decision theory.

**Q2.** Which of the following does not coincide with the purpose of optimal decision-making?

- Profit maximizing
- Cost reduction
- Increasing Profit margins
- Risk maximization

Correct Answer: Option d.

Explanation: The purpose of decision theory is to reduce the risk while taking a decision as much as possible. Risk aversion measures like risk analysis and decision trees are considered for the very sole purpose.

**Q3. **Which of the following is not the situation of decision theory?

- Under certainty
- Under conflict
- Under risk
- Under evaluation

Correct Answer: Option d

Explanation: Under evaluation is not a situation that can have any impact on decision-making. Under certainty, Under risk, and Under conflict is the different situations that can affect the evaluation of action and their outcome. Under certainty, the decision-making is pretty much straightforward, whereas the complexity increases under risk and under uncertainty where the jurisdiction and the ability of managers to access the business environment decide the outcome of the selected course of action.

**Q4. **What is the Laplace if the average of a1 is 23, a2 is 20 a3 is 40 and a4 is 60?

- a1,23
- a2,20
- a3,40
- a4,60

Correct Answer: Option d

Explanation: The Laplace is the maximum of the averages of all the actions thus a4,60 is the Laplace.

**Q5.** What is the maximin if the minimum of actions is a1 is 23, a2 is 20 a3 is 40 and a4 is 60?

- a1,23
- a2,20
- a3,40
- a4,60

Correct Answer: Option d

Explanation: The maximum out of these minimums is a4,60 which is considered in maximin.

## Related Concepts

- Decision making
- Evaluation of alternative
- Choice Theory

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