  We study analogues of $\mathcal{F}$-saturation games, first introduced by
Furedi, Reimer and Seress in 1991, and named as such by West. We examine
analogous games on directed graphs, and show tight results on the walk-avoiding
game. We also examine an intermediate game played on undirected graphs, such
that there exists an orientation avoiding a given family of directed graphs,
and show bounds on the score. This last game is shown to be equivalent to a
recent game studied by Hefetz, Krivelevich, Naor and Stojakovic, and we give
new bounds for biased versions of this game.
