I think by “closest to it” he means “closest to 1000″.
A simpler version would be “pick a natural number, the smallest unique natural number wins”. There’s should be a nash equilibrium for each version, but it would be function of the number of players (and of what happens if nobody picked a unique number—play again? stop?).
As I read it, the problem seems impossible to win? You’re choosing a unique number closest to your chosen to win, which means you can’t win.
I think by “closest to it” he means “closest to 1000″.
A simpler version would be “pick a natural number, the smallest unique natural number wins”. There’s should be a nash equilibrium for each version, but it would be function of the number of players (and of what happens if nobody picked a unique number—play again? stop?).