Invariant games

In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which are variations of Wythoff’s game. The set of P-positions of these games is given by a pair of complementary Beatty sequences related to the irrational quadratic number . We also provide a recursive characterization of this set.