Playing with Subshifts

We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player A) or not (a win for player B). We focus on symbolic dynamical games, where the target set is a subshift. We investigate the relation between the target subshift and the set of turn orders for which A has a winning strategy.