Prisoner's Dilemma

What Is the Prisoner's Dilemma?

The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome.

Key Takeaways

  • A prisoner's dilemma is a situation where individual decision-makers always have an incentive to choose in a way that creates a less than optimal outcome for the individuals as a group.
  • The prisoner's dilemmas occur in many aspects of the economy.
  • People have developed many methods of overcoming prisoner's dilemmas to choose better collective results despite apparently unfavorable individual incentives.

Prisoner's Dilemma

Understanding the Prisoner's Dilemma

The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process. The prisoner's dilemma is one of the most well-known concepts in modern game theory.

The prisoner’s dilemma presents a situation where two parties, separated and unable to communicate, must each choose between co-operating with the other or not. The highest reward for each party occurs when both parties choose to co-operate.

The classic prisoner’s dilemma goes like this:

  • Two members of a gang of bank robbers, Dave and Henry, have been arrested and are being interrogated in separate rooms.
  • The authorities have no other witnesses, and can only prove the case against them if they can convince at least one of the robbers to betray his accomplice and testify to the crime.
  • Each bank robber is faced with the choice to cooperate with his accomplice and remain silent or to defect from the gang and testify for the prosecution.
  • If they both co-operate and remain silent, then the authorities will only be able to convict them on a lesser charge resulting in one year in jail for each (1 year for Dave + 1 year for Henry = 2 years total jail time).
  • If one testifies and the other does not, then the one who testifies will go free and the other will get five years (0 years for the one who defects + 5 for the one convicted = 5 years total).
  • However, if both testify against the other, each will get two years in jail for being partly responsible for the robbery (2 years for Dave + 2 years for Henry = 4 years total jail time).

In this case, each robber always has an incentive to defect, regardless of the choice the other makes. From Dave’s point of view, if Henry remains silent, then Dave can either co-operate with Henry and do a year in jail, or defect and go free. Obviously, he would be better off betraying Henry and the rest of the gang in this case. On the other hand, if Henry defects and testifies against Dave, then Dave’s choice becomes either to remain silent and do five years or to talk and do two years in jail. Again, obviously, he would prefer to do the two years over five.

In both cases, whether Henry cooperates with Dave or defects to the prosecution, Dave will be better off if he himself defects and testifies. Now, since Henry faces the exact same set of choices he also will always be better off defecting as well.

The paradox of the prisoner’s dilemma is this: both robbers can minimize the total jail time that the two of them will do only if they both co-operate and stay silent (2 years total), but the incentives that they each face separately will always drive them each to defect and end up doing the maximum total jail time between the two of them of 4 years total.

Examples of the Prisoner's Dilemma

The economy is replete with examples of prisoner’s dilemmas which can have outcomes that are either beneficial or harmful to the economy and society as a whole. The common thread is this: a situation where the incentives faced by each individual decision-maker would induce them each to behave in a way that makes them all collectively worse off, while individually avoiding choices that would make them all collectively better off if all could some somehow cooperatively choose. 

One such example is the tragedy of the commons. It may be in everyone’s collective advantage to conserve and reinvest in the propagation of a common pool natural resource in order to be able to continue consuming it, but each individual always has an incentive to instead consume as much as possible as quickly as possible, which then depletes the resource. Finding some way to co-operate would clearly make everyone better off here.

On the other hand, the behavior of cartels can be also be considered a prisoner’s dilemma. All members of a cartel can collectively enrich themselves by restricting output to keep the price that each receives high enough to capture economic rents from consumers, but each cartel member individually has an incentive to cheat on the cartel and increase output to also capture rents away from the other cartel members. In terms of the welfare of the overall society that the cartel operates in, this is an example of how a prisoner’s dilemma that breaks the cartel down can sometimes actually make society better off as a whole. 

Escape from the Prisoner's Dilemma

Over time, people have worked out a variety of solutions to prisoner’s dilemmas in order to overcome individual incentives in favor of the common good.

First, in the real world, most economic and other human interactions are repeated more than once. A true prisoner's dilemma is typically played only once or else it is classified as an iterated prisoner's dilemma. In an iterated prisoner’s dilemma, the players can choose strategies that reward cooperation or punish defection over time. By repeatedly interacting with the same individuals we can even deliberately move from a one-time prisoner's dilemma to a repeated prisoner's dilemma.

Second, people have developed formal institutional strategies to alter the incentives that individual decision-makers face. Collective action to enforce cooperative behavior through reputation, rules, laws, democratic or another collective decision making, and explicit social punishment for defections transforms many prisoner’s dilemmas toward the more collectively beneficial cooperative outcomes.  

Last, some people and groups of people have developed psychological and behavioral biases over time such as higher trust in one another, long-term future orientation in repeated interactions, and inclinations toward positive reciprocity of cooperative behavior or negative reciprocity of defecting behaviors. These tendencies may evolve through a kind of natural selection within a society over time or group selection across different competing societies. In effect, they lead groups of individuals to “irrationally” choose outcomes that are actually the most beneficial to all of them together.

Put together, these three factors (the repeated prisoner’s dilemmas, formal institutions that break down prisoner’s dilemmas, and behavioral biases that undermine “rational” individual choice in prisoner’s dilemmas) help resolve the many prisoner’s dilemmas we would all otherwise face.

What Is the Tragedy of the Commons?

The tragedy of the commons is a theoretical problem in economics that proposes every individual has an incentive to consume a resource, but at the expense of every other individual—with no way to exclude anyone from consuming. Generally, the resource of interest is easily available to all individuals without barriers (i.e. the "commons"). This hypothetically leads to over-consumption and ultimately depletion of the common resource, to everybody's detriment. Basically, it highlights the concept of individuals neglecting the well-being of society in the pursuit of personal gain. Its accuracy and application are debated.

What Are Some Ways to Combat the Prisoner's Dilemma?

Solutions to prisoner’s dilemmas focus on overcoming individual incentives in favor of the common good. In the real world most economic and other human interactions are repeated more than once. This allows parties to choose strategies that reward co-operation or punish defection over time.

Another solution relies on developing formal institutional strategies to alter the incentives that individual decision makers face. Finally, behavioral biases will likely develop over time that undermine “rational” individual choice in prisoner’s dilemmas and lead groups of individuals to “irrationally” choose outcomes that are actually the most beneficial to all of them together.

Can the Prisoner's Dilemma Be Useful to Society?

Prisoner's dilemma can sometimes actually make society better off as a whole. A prime example is the behavior of an oil cartel. All cartel members can collectively enrich themselves by restricting output to keep the price of oil at a level where each maximizes revenue received from consumers, but each cartel member individually has an incentive to cheat on the cartel and increase output to also capture revenue away from the other cartel members. The end result is not the optimal outcome that the cartel desires but, rather, an outcome that benefits the consumer in terms of lower oil prices.

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  1. Wiley-Blackwell. "The Real Tragedy of the Commons." Accessed November 22, 2021.

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