The LogiQuad Game System

An intriguing little game, in a pocket format. You place balls of your colour on a grid frame. Or on top of other balls --as long as you own a majority of the four balls on top of which you're placing. You win by having the topmost ball when no more placements are possible. I suspect there may be a Nim-like winning strategy, as the game is completely deterministic and there's gotta be a first-player advantage.