The dual betrayal with its dual five-year sentences is known as the Nash equilibrium of this game, named after mathematician John Nash, one of the pioneers of game theory and the subject of the biopic A Beautiful Mind. The Nash equilibrium is a set of player choices for which a change of strategy by any one player would worsen their outcome. In this case, the Nash equilibrium is the strategy of dual betrayals, because if either player instead chose to remain silent, that player would get a longer sentence. To both get a shorter sentence, they’d have to act cooperatively, coordinating their
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