I am currently interested in a token version of Maker-Breaker positional games. The game is played as Maker-Breaker, but instead of claiming vertices, they both have $k$ tokens and a move consists in moving their token from a vertex to an other vertex on which there is no token. If Maker manage to place a token on all the vertices of an hyperedge, he wins. If Breaker manage to prevent him to do so, he wins.