Each of n players simultaneously choose a positive integer, and one of the players who chose [the least number of [the numbers chosen the fewest times of [the numbers chosen at least once]]] is selected at random and that player wins.

For n=3, the symmetric Nash equilibrium is the player chooses m with probability 1/(2^m).

What is the symmetric Nash equilibrium for n=4? Is it known for general n?

expectit would be unique). $\endgroup$