Two suspects, A and B, are arrested for a crime and placed in separate interrogation rooms. The police lack sufficient evidence to convict them of the main crime but have enough to convict them on a lesser charge. The suspects are offered the following deal:
If one of them confesses and testifies against the other, they will go free while the other will receive a 10-year sentence.
If both confess and testify against each other, they will each receive a 5-year sentence.
If neither confesses, they will each receive a 1-year sentence for a lesser crime.
The suspects cannot communicate with each other. What should they do individually to minimize their collective prison time?
Solution:
This scenario is a classic example of the Prisoner's Dilemma, a concept from game theory. The optimal strategy for each suspect depends on what they believe the other will do.
If suspect A believes that B will confess:
A should confess as well, as it will lead to a 5-year sentence instead of a 10-year sentence.
If suspect A believes that B will remain silent:
A should still confess, as it leads to either going free (if B remains silent) or a 5-year sentence (if B also confesses).
The same logic applies to suspect B:
If B believes that A will confess, B should confess as well.
If B believes that A will remain silent, B should confess to avoid the 10-year sentence if A decides to confess.
In summary, given the lack of communication between the suspects and their rational self-interest, the most likely outcome is that both suspects will confess, resulting in a 5-year sentence each, even though the collectively optimal outcome would be for neither of them to confess.
