Game playing is for teen agers. There are subtle ways of asking what he wants.

I once dated a woman three times, and the forth time she got all nervous about something. I had to insist that she tell me what the problem was, and she finally said "We have dated three times now, and you haven't tried to get me into bed."
I didn't tell her that the reason was I didn't know if I wanted to see her again. That did it, never saw her again.

If he wants to "see more of you" he will give you a sign. Most men make that sign very clear. If you see that sign, ask him if he would like to stay the night. His answer will tell you all you need to know.