Prisoner's Dilemma

By WILLIAM POUNDSTONE

[Albert] Tucker was a distinguished Princeton mathematician who knew both von Neumann and Nash (Nash was one of Tucker's students at Princeton).

... Tucker devised a now-well-known dilemma tale and coined the name, "prisoner's dilemma." ...

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to three years in jail.

The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered the very same deal. Each prisoner is concerned only with his own welfare--with minimizing his own prison sentence.

The prisoners can reason as follows: "Suppose I testify and the other prisoner doesn't. Then I get off scot-free (rather than spending a year in jail). Suppose I testify and the other prisoner does too. Then I get two years (rather than three). Either way I'm better off turning state's evidence. Testifying takes a year off my sentence, no matter what the other guy does."

The trouble is, the other prisoner can and will come to the very same conclusion. If both parties are rational, both will testify and both will get two years in jail. If only they had both refused to testify, they would have gotten just a year each!

Tucker's story was not intended to be a realistic picture of criminology. It's interesting, then, that some corrections experts' misgivings about plea bargaining complain of real-life prisoner's dilemmas. It takes an overwhelmingly strong case to secure a death penalty. Not only must the evidence show that the suspect committed the murder but it must also indicate that the crime was committed in "cold blood." In practice, death penalty (as opposed to life imprisonment) convictions often hinge on the testimony of an accomplice who was in on the plans for the crime. In connection with the death sentence of child murderer Robert Alton Harris, the Los Angeles Times wrote (January 29, 1990):

In robberies where murders occur, for example, there is often more than one criminal involved and thus more than one person who may be eligible for the death penalty. But for a prosecutor, "what's important is that you score one touchdown," in the form of a death sentence, said Franklin R. Zimring, UC Berkeley law professor and a capital punishment expert.

Frequently, a race ensues in which the robbers try to be the first to point the finger at an accomplice and make a deal with the prosecutor to testify in return for leniency.

Sometimes, Zimring said, it never becomes clear whether the person who got leniency or the person on trial for his life actually pulled the trigger.