We have these discussions all the time on J9s threads about how these feel like games. I work with Doctors and Scientists and I look at it more like a protocol. For different studies you have to follow different protocols. You can also change the protocol once you gather more information.
I think it feels like games to some people because you are intentionally not contacting someone when you really want to contact them. What you are really trying to do is fill your schedule up with activities, work, exercise, kids that you really don't have time to blow up someones phone. Then it's not a game you are just extremely busy.
You can be true to yourself and send 10 texts before a response if you truly feel that is the right thing to do, but unfortunately most confident, successful women are going to find that as a turn off.
Take this new opportunity slow, keep your options open and live in the moment.