Changes in Representation which Preserve Strategies in Games

One reason for changing the representation of a game is to make it similar to a previously solved one. As a def in i t ion of s im i la r i t y , people have previously often proposed homomorphism-like structures. One such structure, the "s -homomorphism", is defined and studied in this paper. It is indicated that a useful winning s t rategy exists for any game in a general class cal led, "positional games". A set of suf f ic ient conditions is derived which a game has to f u l f i l l to have an s0-homomorphism with a positional game. The conditions are exemplified by applying it to a class of games shown by Newell to be representable as t ic tactoe.