N players are competing for a prize of 20 dollars Who wins t

N players are competing for a prize of 20 dollars. Who wins the prize is determined as
follows. Each player submits a real number between 0 and 100 simultaneously. A player
wins if his number is the closest to 2/3 of the average of the numbers of all N participants.
If two players tie, then they split the prize. If all the participants are rational, what guess
will each participant submit?

Solution

If two players tie, then they split the prize. If all the participants are rational, what guess will each participant submit

yes, because the probability to win for each participant is less than the average