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# Prisoner’s Dilemma

Updated on April 17, 2024
Article bySusmita Pathak
Edited bySusmita Pathak
Reviewed byDheeraj Vaidya, CFA, FRM

## Prisoner’s Dilemma Definition

The prisoner’s dilemma refers to a paradox in the decision-making and modern game theory that exemplifies how two rational individuals trapped in the same situation are likely to respond to it without knowing other’s take on the same. They either act in their self-interests or refuse to cooperate, leading to a sub-optimal or non-optimal outcome.

It also allows self-interested individuals to know the possibility of cooperation in settings where strategic decision-making is occurring. Whether it is a game or real-life scenario, this notion helps analyze all possible outcomes of a problem and make the best decision to come out of it. And for that reason, it is applicable in different niches, including business, , finance, politics, philosophy, psychology, sociology, etc.

For eg:
Source: Prisoner’s Dilemma (wallstreetmojo.com)

### Key Takeaways

• The prisoner’s dilemma is a paradox in modern game theory and decision-making. In this situation, two rational participants cooperate or betray each other to reach an optimal result.
• The notion was developed in 1950 by mathematicians Merrill Flood and Melvin Dresher and was further explored and named by another mathematician Albert William Tucker.
• This game theory scenario happens to be such that it enables both individuals to understand that decisions taken in their self-interests do not necessarily prove to be the best ones.
• Compelling choices or incentives, maintaining proper communication, and understanding the outcome of cooperation and defection can help avoid the prisoner’s paradox.

### How Does Prisoner’s Dilemma Work?

The prisoner’s dilemma theory describes a situation in which two participants must choose between cooperating or not in the decision-making process to reach an optimal solution. Cooperation helps make decisions in the best interests of the individual, business or economics, or society.

Because these parties cannot communicate about the situation, they act in their self-interests rather than cooperating to protect themselves. As a result, a less than optimal or worse outcome occurs, which impacts both participants. This approach takes place such that it enables individuals or entities to understand that decisions made in self-interest are not always the best.

Mathematicians Merrill Flood and Melvin Dresher developed the first prisoner’s dilemma game in 1950 while working at RAND Corp. However, Albert William Tucker, a Canadian mathematician, gave this paradox game theory situation its name.

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### Classic Prisoner’s Dilemma Situation

Consider the following scenario with two criminal suspects, A and B. They are apprehended by the police and placed in two different rooms or cells. The cops, finding it hard to obtain confessions, try to trick them both with a deal. They ask them to confess (defect) or blame the other partner or cooperate to save themselves. In this situation, there are four possible outcomes:

• Both A and B confess or defect and get two years in prison each.
• A blames B. A is released while B gets three years in prison.
• B blames A. A is subject to a three-year jail term while B is set free.
• Both A and B cooperate and remain silent. Each of them gets one year in prison on a lesser charge.

These possible outcomes suggest that if both A and B decide to be selfish to avoid imprisonment, they will blame each other. It will prove each other’s involvement in the crime committed. As a result, they will have to face a jail term of three years each.

The act of blaming each other will demonstrate a rational decision and provide the prisoner’s dilemma , regardless of the worse outcome. However, assuming that both will confess or defect without knowing that the other did the same will land each in prison for two years.

On the other hand, if both suspects cooperate and remain silent, the imprisonment tenure would only be one year.

This classic scenario reveals how behaving in one’s self-interest results in a poor outcome than cooperating.

### Prisoner’s Dilemma In Business & Economics

The game theory prisoner’s dilemma perfectly defines decision-making in business and economics. Communication makes decision-making easier and mutually beneficial. The possible outcomes help companies determine the best solution to problems that arise. Unfortunately, in this approach, the two parties do not get the opportunity to share their perspectives on the matter.

Let us say TEE and COFF are two beverage companies competing in the same local market. To make sure one remains ahead of the other, they try to figure out ways to improve their sales. Hence, they apply the prisoner’s paradox notion to decide whether investing in advertisements is worthwhile. Keeping into consideration the events expected to occur, the possible outcomes could be:

• If TEE and COFF advertise their products, customers will split between the brands in 50-50 proportions. With the advertising costs deducted separately, the revenue generated would be equal.
• If TEE advertises (defects) and COFF does not (cooperate), 80% of the population will buy the former’s product. Though it will generate more profits, the advertising cost would get deducted from the .
• If COFF advertises and TEE does not, 80% of the population will buy COFF’s product. Though the revenue would be more for the brand, the advertising cost would get deducted from it.
• If TEE and COFF do not advertise, it is likely for 50% of the population to go for TEE’s products. And the other 50% to opt for COFF’s product. It, in turn, would mean equal distribution of revenue between the two brands.

For eg:
Source: Prisoner’s Dilemma (wallstreetmojo.com)

The best thing for both brands to keep up with the competition would be not to advertise their products. However, as individual parties, they would find it more relevant to focus on their self-interests. Hence, both will promote their products even if the other brand is not doing so.

Unlike suspects in the classic prisoner’s paradox scenario, these two brands get an opportunity to influence each other. They finally decide on whether they would be advertising their products. It lets them achieve the prisoner’s dilemma Nash equilibrium.

#### In Economics

Today, every country wants to minimize the environmental damage due to pollution and global warming. However, cooperation needs to come from every economy around the world. In this situation, there are four possible outcomes under the prisoner’s paradox:

• All the countries agree and put efforts to tackle environmental issues and control the situation post restrictions.
• 80% of the world population cooperates and achieves good results.
• 20% of the world population participates with no significant results, leading to wastage of effort and resources.
• All the countries cheat each other and refrain from taking any responsibility and putting effort. As a result, they do not do anything to control the environmental damage.

Any of these environmental decisions will directly impact the global economy. The reason is that natural resources, such as minerals and fossil fuels, act as a direct input into industrial production.

### Prisoner’s Dilemma Examples

Let us consider the following prisoner’s dilemma examples to understand the concept better:

#### Example #1

Researchers have declared the COVID-19 pandemic to be a clear case of the prisoner’s paradox. It is because the effectiveness of vaccination is highly dependent on individual choices. They also highlight the cooperation and defect proportion in this scenario.

The research shows how the rate of infected people can reduce if everyone around the globe cooperates and follows the public health guidelines, including wearing masks, maintaining social distance, washing hands frequently, and staying at home.

And then comes the defect situation where some individuals will find washing hands a tedious task, masks annoying, and hugging an everyday routine. Furthermore, they will also find getting jabbed doubtful.

#### Example #2

The OPEC+ countries and the United States shale producers are the driving forces behind the oil market. While Saudi Arabia functions as an enforcer for the former, investors act as enforcers for the latter.

The prisoner’s paradox is quite evident in the oil sector, where cooperation between all participants leads to a mutual outcome. However, when all parties agree to cooperate, cheating with the rising oil prices seems to be the best option for individual actors. But if every participant acts in their self-interests, everyone loses.

### How To Avoid Prisoner’s Dilemma?

There are a few approaches to avoid the prisoner’s paradox while still serving the individual demands of market participants and the global economy. Some of them are as follows:

For eg:
Source: Prisoner’s Dilemma (wallstreetmojo.com)

• Designing incentives for different participants in such a way that the optimal outcome still seems beneficial to individual decision-makers
• Establishing communication in real-life scenarios where participants get an opportunity to interact and influence each other for better decision-making
• Remaining cooperative as cooperation leads to better results, while defection yields a minimal effect

What is prisoner’s dilemma?

The prisoner’s paradox or dilemma is a situation in game theory in which two parties decide whether to cooperate or betray each other to achieve optimal results. It applies to business, economics, finance, politics, philosophy, psychology, and sociology.

How can a business use the prisoner’s dilemma?

Businesses can use the prisoner’s paradox or dilemma to determine the best way for resolving a problem by identifying the possible outcomes of each planned event.

What is Nash Equilibrium in prisoner’s dilemma?

The prisoner’s dilemma Nash Equilibrium is achieved when each participant strategizes procedures and actions in light of the decisions that the other player in the situation can make. In such a scenario, either every individual cooperates and wins or betrays the other, leading to a collective loss.

This has been a guide to Prisoner’s Dilemma and its definition. Here we discuss how to avoid and how does prisoner’s dilemma works, along with examples. You may also have a look at the following articles to learn more –