# Prisoners’ Dilemma

A decision-making and game theory paradox that illustrates the decisions of two rational individuals cannot result in an optimal solution

# What is Prisoner’s Dilemma?

A prisoner’s dilemma is a decision-making and game theory paradox illustrating that two rational individuals making decisions in their own self-interest cannot result in an optimal solution. The paradox was developed by mathematicians M. Flood an M. Dresher in 1950, and the modern interpretation was conceptualized by Canadian mathematician A.W. Tucker.

The prisoner’s dilemma shows that in a non-cooperative situation, even a more attractive strategy can lead to worse results.

### Prisoner’s dilemma scenario

Imagine that the police arrested two suspects of a crime. Both suspects are held in different cells and they cannot communicate with each other. The police officer offers to both suspects the opportunity to either remain silent or blame another suspect. If both suspects remain silent, they both will serve only one year in prison. If they both blame each other, they both will serve three years in prison.

If one of the suspects blames another and the other remains silent, the suspect who remained silent would serve five years in prison, while another suspect would be set free. The table below shows the possible payoffs:

### Prisoner’s dilemma explained

In such a setting, both suspects do not know the decision chosen by another suspect. Therefore, the most rational decision from the perspective of self-interest is to blame the other suspect.

For example, suspect A is afraid of remaining silent because in such a case, he can receive five years in prison if suspect B blames him. If suspect A chooses to blame suspect B, he can be set free if suspect B remains silent. However, it is not likely, because suspect B is using the same rationale and he is also going to blame suspect A.

Although the decision of remaining silent by both suspects provides the more optimal payoff, it is not a rational option because both parties behave in their self-interest. On the other hand, the decision of blaming another suspect is a rational decision from that perspective and it provides Nash equilibrium despite the worse payoff. Learn how scenarios like this affect market behavior on CFI’s Behavioral Finance Fundamentals Course.