The prisoner’s dilemma in Game theory

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

Let’s analyze the nature of the dilemma assuming that both understand the nature of the game, and that despite being members of the same gang, they have no loyalty to each other and will have no opportunity for retribution or reward outside the game.

Prisoner B stays silent Prisoner B betrays
Prisoner A stays silent Each serves 1 year Prisoner A: 3 years
Prisoner B: goes free
Prisoner A betrays Prisoner A: goes free
Prisoner B: 3 years
Each serves 2 years

Please try to think over the solution for a while and analyze each case yourself.
By analyzing the table, we can see that:
You are always punished less for choosing to betray the other person. However, as a group, both of you fare better by cooperating(remaining silent).
Think over the above statement for a while.
If you have a problem in analyzing this then you can watch this video: Khan Academy’s explanation

This is the dilemma both the prisoner’s face. Should one cooperate or betray?
Even if the best solution would be both the prisoners cooperating with each other, but due to uncertainty on each other both of them betray each other getting a lesser optimum solution.
This can be observed in may real-life cases like:

The prisoner’s dilemma demonstrates that two rational people might not cooperate even if it is in their best interest to do so. Just keep looking around in this beautiful world. Who knows you can find yourself in a prisoner’s dilemma one day!



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