[ExI] 2/3 game again

spike spike66 at att.net
Thu Jul 30 04:23:00 UTC 2009


I have been thinking some more about the 2/3 game, in which the players
choose any number between 0 and 100 inclusive, not necessarily an integer.
The variation I chose was to have everyone's guess visible.  Damien and
Emlyn won everlasting esteem in that round as I recall, altho Damien gets
esteem for only half of eternity because he actually won by meta-mistake.
He estimated the average and forgot to multiply by 2/3, but was saved by his
countryman in a most clever sacrifice play.  

Another paradox-inducing version is one where the winner is closest to 2/3
the average of the others, either above or below, but the other guesses are
not visible.  This version leads to a delightfully diabolical paradox.  It
would be illogical to guess higher than 66.667, for this would be better
than 67 even if *all* the other players guess 100.  Right?  

But all the other players will not guess 100 of course, for they would do
the same calculus that I just did, and guess no higher than 66.667 in which
case the best possible guess is 44.444, but of course the others will reason
likewise, so on it goes all the way down to... zero!

But zero isn't the best answer, because everyone will not reason all the way
down; some will stop at some intermediate value.

What value?


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