When is it worth trusting someone?
As they say, “Trust makes the way for treachery.” But is this true?
For a puzzle that suggests an answer¹…use the DOOR.
Two prisoners are suspected of carrying out a crime together.
The maximum sentence for the crime is 10 years.
The two suspects have been arrested separately, and each is offered the same deal: If Suspect 1 confesses that they both committed the crime and Suspect 2 remains silent, the charges against him will be dropped–but his accomplice will have to serve the full 10 years.
If both suspects remain silent, there will only be circumstantial evidence, which nonetheless will put both men behind bars for 2 years.
But if both confess to the crime, they will both be sentenced to 5 years in prison.
The suspects cannot confer. How should they react under questioning? Should they trust each other?
This is the so-called prisoner’s dilemma, a classic conundrum in game theory. The two suspects both lose if they opt for the most obvious solution–i.e. to put themselves first first: They each get a 5-year sentence. They fare better if each one trusts the other to remain silent: Then it’s only 2 years each. Note also that if only one of the suspects confesses, the other gets 10 years while he himself goes free.
In 1979 the political scientist Robert Axelrod organized a tournament in which 14 colleagues played 200 rounds of the Prisoner’s Dilemma against one another in order to work out the best strategy. He found that in the first round it is best to cooperate with your accomplice (i.e. trust him). In the second round, do what the accomplice did in the previous round. By imitating his moves, he will follow yours.
¹ The Decision Book: Fifty Models for Strategic Thinking by Mikael Krogerus and Roman Tschappeler (Profile Books, 2011) pp. 124-125. Structure of the paragraphs and other features slightly altered.