Platonia dilemma

A similar game, referred to as a “Luring Lottery”, was actually played by the editors of Scientific American 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 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 his or her 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 becomes a dubious strategy.

…

Although the magazine had previously discussed the concept of superrationality 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 googolplex). Some took this game further by filling their postcards with mathematical expressions designed to evaluate to the largest possible number in the limited space allowed. The magazine was unable to tell who won, and the monetary value of the prize would have been a minuscule fraction of a cent.

In related sightseeing, I just read that a real-life experiment found that 40% of participants will take the “cooperate” (ie: irrational) option in Prisoner’s Dilemma.