I have this issue for over a year now, that i cannot play a game in blender game engine in fullscreen mode. The fps drops after a few seconds down to 12 and i had no clue why, it even did this with a completely empty scene.
Well not anymore! The solution is to disable the ‘use frame rate’ in the render panel under system.
I’m so happy that i found the solution to my problem after all those time. (//edit: better to turn of vsync instead (located next to that option))
Here is the problem/fps drop in action.
Now the question will be: How good/bad is it to disable that setting?