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dollars divided by the total number of entries received, to be awarded to the submitter of a randomly chosen entry. Thus a reader who submitted a large number of entries increased their chances of winning but reduced the maximum possible value of the prize. It can be shown mathematically that one maximizes one's average winnings in this game by submitting a number of entries equal to the total number of entries of others. Of course, if others take this into account, then this strategy translates into a runaway reaction to unbounded number of entries being submitted.
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33:, an eccentric trillionaire gathers 20 people together, and tells them that if one and only one of them sends them a telegram (reverse charges) 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
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with the number of sides equal to the number of expected responders (about 5% of the readership), and then send "1" if you roll "1". If all contestants had followed this strategy, it is possible that the magazine would have received a single postcard, with a "1", and would have had to pay a million
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in the 1980s. To enter the contest once, readers had to send in a postcard with the number "1" written on it. They were also explicitly permitted to submit as many entries as they wished by sending in a single postcard bearing the number of entries they wished to submit. The prize was one million
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from which the above-mentioned algorithm can be deduced, many of the contestants submitted entries consisting of an astronomically large number (including several who entered a
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dollars to the sender of that postcard. Reputedly the publisher and owners were very concerned about betting the company on a game.
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Hofstadter, Douglas (June 1983). "Dilemmas for
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A similar game, referred to as a "Luring
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Hofstadter, Douglas (September 1983). "Irrationality Is the Square Root of All Evil".
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William
Poundstone, Prisoner's Dilemma, Doubleday, NY 1992, pp. 272–276.
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Game theory introduced in
Douglas Hofstadter's book Metamagical Themas
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Although the magazine had previously discussed the concept of
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thing to do is to send a telegram with probability 1/20.
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276:Fluid Concepts and Creative Analogies
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168:. Basic Books. pp. 756–766.
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416:Indiana University Bloomington
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162:Hofstadter, Douglas (1985).
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