Prisoner’s Dilemma

The prisoner’s dilemma is a fundamental problem in game theory that demonstrates why two people might not cooperate even if it is in both their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name.

A classic example of the prisoner's dilemma (PD) is presented as follows:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full one-year sentence. If both remain silent, both prisoners are sentenced to only one month in jail for a minor charge. If each betrays the other, each receives a three-month sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

The classical prisoner's dilemma can be summarized thus:

Imagine you are player A. If player B decides to stay silent about committing the crime then you are better off confessing, because then you will get off free. Similarly, if player B confesses then you will be better off confessing, since then you get a sentence of 3 months rather than a sentence of 1 year. From this point of view, regardless of what player B does, as player A you are better off confessing. One says that confessing (defecting) is the dominant strategy. As Prisoner A, you can accurately say, "No matter what Prisoner B does, I personally am better off confessing than staying silent. Therefore, for my own sake, I should confess." However, if the other player acts similarly then you both confess and both get a worse sentence than you would have gotten by both staying silent. That is, the seemingly rational self-interested decisions lead to worse sentences—hence the seeming dilemma.

Although they are not permitted to communicate, if the prisoners trust each other then they can both rationally choose to remain silent, lessening the penalty for both of them. This particular example, involving prisoners may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics and sociology, as well as to evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.

In politics

In political science, for instance, the PD scenario is often used to illustrate the problem of two states engaged in an arms race. Both will reason that they have two options, either to increase military expenditure or to make an agreement to reduce weapons. Either state will benefit from military expansion regardless of what the other state does; therefore, they both incline towards military expansion. The paradox is that both states are acting rationally, but producing an apparently irrational result.

In environmental studies

In environmental studies, the PD is evident in crises such as global climate change. All countries will benefit from a stable climate, but any single country is often hesitant to curb CO₂ emissions. The immediate benefit to an individual country to maintain current behaviour is perceived to be greater than the eventual benefit to all countries if behaviour was changed, therefore explaining the current impasse concerning climate change.

In psychology

In addiction research/behavioural economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome, and that defecting both today and in the future is the worst outcome. The case where one abstains today but relapses in the future is clearly a bad outcome—in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). The final case, where one engages in the addictive behaviour today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs), there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.

In economics

Advertising is sometimes cited as a real life example of the prisoner’s dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A’s advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period the advertising cancels out, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes.

Sometimes cooperative behaviour does emerge in business situations. For instance, cigarette manufacturers endorsed the creation of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.

Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoners' dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly stealing business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.

In law

The theoretical conclusion of PD is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the PD scenario applies: it is in the interest of both suspects to confess and testify against the other prisoner/suspect, even if each is innocent of the alleged crime.