The game you're looking for is Funny Friends, by Friedemann Friese. The US reprint is censored, however, as the game allows you to have gay relationships, can encourage you to join a cult, take drugs, have threesomes, etc. Great, great game but, um, needs fairly broadminded players. For example, you're rated on your…

FFG have also coded the aliens so you know in which phase of the game turn the alien's power is active. I really, really need to play it more (one of my regular players had a bad experience with it, so we have to try again with people who are on board with its style.)

Depressingly obsessed boardgamer here: