but when _refugee_ decides not to initiate texting -- she perceives herself to have less "power" in the relationship dance than the other person.

It's more complicated than that.

When Refugee decides not to initiate texting she's starting the bid at "I matter more to you than you matter to me." Obviously, if the other person bids an equal amount, the relationship is deadlocked.

What follows is ornate and complicated. Just google "3 day rule" to see how complicated. The short version is that it is assumed that women are going to play the "I matter more to you than you matter to me" card because tradition. Men, therefore, must play the "you matter to me but not so much that I'm going to demonstrate it to you" card. Note that this is just second contact. The whole tawdry affair rockets through an untold number of iterations until the couple is truly a couple... and sometimes, well past that point.

It's a power dynamic. Both people want to be together but it's important to establish the shape and bounds of that dynamic. It basically gives you a starting point from which to explore each other, and it's anything but solvable by inspection. Thus my statement: the people who know how to do this end up with people who know how to do this. The people who don't end up with each other. And the people who understand the game, are willing to put in the time, and recognize that it is a game but that the score does matter tend to be better at resolving relationship issues because they accepted more of them at the get-go.

With shy people, there is much less of a power dynamic.

Disagree. Wit shy people the power dynamic is a lot more passive-aggressive. Both people are still telegraphing the same subtext, they're just doing it in a clumsy fashion.