You said sorry. She seemed satisfied. Two weeks later, same fight.
The game
She wants resolution: acknowledgment of what happened, some signal it won't repeat. You want the conversation to end. The apology does both jobs at once: it closes the loop for her and gets you out.
It costs you a small concession to say the words. She gets what sounds like resolution. The conversation ends and you move on, while she's left waiting to see if anything actually changes.
The equilibrium
She learns that pressing hard enough gets an apology. You learn the apology ends it. The fight keeps recurring because nothing changed, and she starts to sense (even if she can't name it) that you're not engaging with what she's saying. That feeling compounds faster than the original issue.
Dominated strategies
The fake apology.
It ends the conversation. But you've trained her that escalating is how she gets acknowledgment. You've confirmed you check out under pressure. And the issue she raised didn't go anywhere. It went underground, where it picks up weight. By the time it surfaces again, it's heavier, and the relationship has less capacity to absorb it.
She can sense it before she can name it: that you're saying the words without engaging with what she's saying. That feeling compounds faster than the original issue. The fight keeps coming back not because she won't let it go, but because nothing actually changed.
The shorter conversation (the one where you say what you actually think happened, even if it isn't "I was wrong") has a chance of ending the pattern. The apology just moves it.