sometimes the world "for" means "of" it's just a auxiliary word .there are something for you "这有你的一些东西"。
sometimes it means"for the sake of"为了。“i'll do everything for you”"我为了你会做任何事"。
a question about the sentence"new computer games for his ps2",the world "for" ,it's just a auxiliary word.the meaning of sentence i,i can't explain it.because it is irrationality. it may be a ps2 game .may be a comeputer game.they are two different things.