OP, I doubt it's for any type of power positioning. Women have too many options in the dating scene. Even a mediocre woman will have her inbox filled with DMs and txts from dudes. After one single date, you have yet to make a big enough impact on them to try and gain power in the relationship. They just don't care enough yet. Unless you are Brad Pitt, or a 10 yourself, a woman does not care to make you chase after the first date. They already have too many options chasing them.
More often than not, the simple answer to a girl pulling back after the first date is: a better option came along. Always keep in mind, a woman's hypergamous nature is their innate drive. A single date is not enough for a woman to become bound to you; in fact, this normally doesn't happen until numerous dates spanning over a couple months takes place. You may illicit extremely high interest from her by being on top of your game during the date, however women are creatures of the moment. In that moment, you may be number #1 on her roster..but the very next day, another big man, or 2 or 3, may have come along and knocked you off your rung on her ladder.
Do not try to figure out what happened. Never chase a woman whose interest has waned..for whatever reason. Chasing will only lower their interest even more. Instead, go about your life, continue going on more first dates, talk to more women, focus on self improvement. And when you feel like touching bases with her a week or two, then do so. You never know what's going on in a person's life. She may not be interested in going on a second date with you that week...but whose to say the following week won't be different. Big man #s 2-4 may have royaly ****ed up and you're back to #1. It's not your job as a man to try to figure out what's going on in their life, or their head....not after just one single date. All you can do is continue to function as a man should..which is keep going on dates, keep talking to women, keep going about your business, and keep pursuing your goals in life. Sooner or later, you will meet a woman who does see you as #1, and won't knock you down any rungs because you are so high up. You will have made such an impact on her attraction, that she may begin to play games and make you chase or start **** testing you. But this is more than likely not after one single date. Stop worrying about one single woman so much OP, and keep at it.