Platonia dilemma

Game theory introduced in Douglas Hofstadter's book Metamagical Themas

In the platonia dilemma introduced in Douglas Hofstadter's book Metamagical Themas, an eccentric trillionaire gathers 20 people together, and tells them that if one and only one of them sends them a telegram by noon the next day, that person will receive a billion dollars. If they receive more than one telegram, or none at all, no one will get any money, and cooperation between players is forbidden. In this situation, the superrational thing to do is to send a telegram with probability 1/20.

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