  We study a variation of the combinatorial game of 2-pile Nim. Move as in
2-pile Nim but with the following constraint:
  Suppose the previous player has just removed say $x>0$ tokens from the
shorter pile (either pile in case they have the same height). If the next
player now removes $x$ tokens from the larger pile, then he imitates his
opponent. For a predetermined natural number $p$, by the rules of the game,
neither player is allowed to imitate his opponent on more than $p-1$
consecutive moves.
  We prove that the strategy of this game resembles closely that of a variant
of Wythoff Nim--a variant with a blocking manoeuvre on $p-1$ diagonal
positions. In fact, we show a slightly more general result in which we have
relaxed the notion of what an imitation is.
