Invariant games

Eric Duchene (1) , Michel Rigo (2)

1 LIESP - Laboratoire d'Informatique pour l'Entreprise et les Systèmes de Production
2 Université de Liège

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 are given by a pair of complementary Beatty sequences related to the irrational quadratic number k = (1; 1, k). We also provide a recursive characterization of this set.

Domaines: Mathématique discrète [cs.DM]

Eric Duchene, Michel Rigo. Invariant games. Theoretical Computer Science, 2009. ⟨hal-00408013⟩