v 6.10.00
20 Jun 2020
updated 6 Jan 2021

Understanding the Prisoner's Dilemma

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 of loitering, which will mean one year in jail 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 three years (0 years for the one who defects + 3 for the one convicted = 3 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 three years or to talk and do two years in jail. Again, obviously, he would prefer to do the two years over three.

In both cases, whether Henry co-operates 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 (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 (4 years total).