Once upon a time, a pianist was arrested by the secret police and accused of spying. He was carrying sheets of paper covered with a mysterious code. Despite protesting that it was merely the sheet music for Beethoven’s Moonlight Sonata, the poor man was marched to the cells. A couple of hours later, a sinister interrogator walked in. “You’d better tell us everything, comrade,” he announced with a thin smile. “We have caught your friend Beethoven. He is already talking.”

This sets up the most famous problem in game theory: the prisoner’s dilemma. The interrogator explains that if one man confesses and the other does not, the talkative prisoner will go free and the other will do 25 years in a gulag. If they both remain silent, they will each spend five years in prison. If they both confess, 20 years each. The dilemma is clear enough: each would do better to confess, regardless of what the other does; yet collectively they could profit by sticking together.

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