Dating
You've been more obsessed with her than with anyone you've dated, including people you were more compatible with, more attracted to, who treated you better. She's not consistent. Some weeks she's all in, texting constantly, making plans, acting like you're the only person she wants to see. Then she goes quiet. No explanation. When she comes back, it's warm again.
The inconsistency is the mechanism.
The game
Behavioral research established decades ago that unpredictable rewards create stronger compulsion than consistent ones. A slot machine that pays out randomly is harder to walk away from than one that pays out every time, even if the total payout is identical. The unpredictability is what keeps you playing.
The same logic applies here. When her warmth is reliable, you can calibrate. You know what you have, you can decide how much to invest, you can take it or leave it. When it's unpredictable, you can't calibrate. Every cold phase raises the question of what changed. Every warm phase feels like a reward you worked for.
She has two strategies: be consistently warm, or vary it. Consistent warmth gives you information and control. Variable warmth keeps you uncertain and invested.
The equilibrium
This pattern doesn't require strategy on her part. It just requires that she follow her actual feelings, which fluctuate. The game settles here because it works. You're more engaged than you would be with someone more consistent. The hot phases keep you in; the cold phases keep you trying.
From her side, the variability may be genuine. She may not be managing anything. The effect on you is the same either way.
Dominated strategies
Trying harder during the cold phases is the dominated strategy. More effort during a cold phase doesn't shorten it. If anything, it confirms that the pattern works on you, and raises the cost of the next one you'll have to endure.
The variable reward schedule only works if you keep playing. The one move that disrupts it is being willing to leave during a cold phase and genuinely meaning it, not deploying it as a counter-tactic. Consistent warmth from someone less exciting is worth more, in practice, than unpredictable intensity from someone who has you checking your phone.