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?).
A game similar to Guess 2/3 of the average,
Choose a number below 1000.
Unique number closest to it wins. (People with same answer are eliminated)
What is your pick and the reason for your choice?