The Plutonia Dilemma

Since finishing Rheingold's Smart Mobs, I've been delving more into game theory and cooperation. One amusing article I've read is the Plutonia Dilemma. Makes you wonder what possible kinds of implicit and explicit cooperation we can build into next-generation ubicomp systems.


In the plutonia 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 him a telegram (reverse charges) by noon the next day, that person will receive a billion dollars. If he receives 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.

A similar game was actually played by the editors of Scientific American in the 1980s. The editor of Mathematical Recreations offered a very large prize, the net worth of the magazine divided by the largest number submitted, to be awarded to the person submitting the largest number.

According to the magazine, the rational thing was for each contestant to roll a simulated die 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". Reputedly the publisher and owners were very concerned about betting the company on a game. Despite publishing this algorithm, one of the contestants submitted an entry consisting of an astronomically large number, googolplex. The owners retained their interest, and the winner received a check for $0.01 - the smallest printable by the accounting system.


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