Is there a name for the following combinatorial game? Is there a solution which player has a winning strategy?

Basically this game is "sprouts without midpoints". One starts with $n$ points in the plane. Then a move consists of joining two points (it is also allowed to join a point with itself, i.e. to make loops). The lines are not allowed to intersect, i.e. the graph should be planar. The degree of each point is supposed to be $\leq 3$. Thus, points of degree $3$ are "dead". The player with the last move wins.

I have already determined some game outcomes, but wanted to know a reference. On the german Wikipedia it says that the sprouts variant where the players may decide if they add a midpoint is already solved (the first player wins) and "known" as black-and-white sprouts, but I could not find anything about this, and also this game has different game outcomes than the game described above.