Something like that could work, but it seems like you would still need to have a rule that you must guess before you know the other players guesses.
Otherwise, player 2 could simply guess the same mean as player 1 - with a slightly larger standard deviation—and have a PDF that takes a higher value everywhere except for a very small interval around the mean itself.
Alternatively, if 3 players all guessed the same standard deviation, and the means they guessed were 49, 50, and 51, then we would have the same problem that the opening post mentions in the first place.
Something like that could work, but it seems like you would still need to have a rule that you must guess before you know the other players guesses.
Otherwise, player 2 could simply guess the same mean as player 1 - with a slightly larger standard deviation—and have a PDF that takes a higher value everywhere except for a very small interval around the mean itself.
Alternatively, if 3 players all guessed the same standard deviation, and the means they guessed were 49, 50, and 51, then we would have the same problem that the opening post mentions in the first place.