Invariant games

Authors:
Eric Duchêne;Michel Rigo
Affiliations:
Laboratoire LIESP, Univ. Claude Bernard Lyon 1, Bâtiment Nautibus (ex 710), 843, Bd. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France;Institute of Mathematics, University of Liège, Grande Traverse 12 (B37), B-4000 Liège, Belgium
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

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 @a"k=(1;1,k@?). We also provide a recursive characterization of this set.