She mentions a guy from work. Nothing dramatic: he's been texting her, she thinks he likes her, she doesn't know what to do about it. She seems a little pleased by it. You find yourself more attentive that week. You text first. You make a plan.
You know what happened. You're still doing it.
The game
She has two moves: share information about outside interest, or not. You have two moves: compete, or don't.
When she signals that someone else is interested, you get less certain about where you stand. Certainty is what lets you coast. Remove it and effort comes back. She gets more of you without having to give more of herself. The information cost her nothing.
Your position is awkward because the threat might be real. If she's genuinely being pursued and you don't respond, you might actually lose her. So competing feels justified. The problem is that competing confirms the signal worked, which means it'll get used again.
The equilibrium
What keeps this stable is that you can't easily tell whether the information was offered deliberately or just mentioned. "He keeps texting me" looks the same either way. You can't discount it without risking that it's real. So you respond to it, which is exactly what responding to it produces.
The dynamic that emerges: she holds low-level uncertainty over the relationship, you work to close it, it never fully closes.
Dominated strategies
Competing directly every time it comes up. More attention, more effort, more investment. This works in the short term and teaches her that the signal produces results. The next one will come sooner.
Trying to run the same thing back. Mentioning your own outside interest to rebalance the leverage. If it's a tactic on her side, this escalates it into a contest. If it wasn't, you've introduced something that wasn't there.
The move that actually changes the structure: have real options. Not as a counter-tactic — as an actual thing. Someone who's genuinely in demand doesn't need to compete when a signal appears. They already know their position. That's what she was simulating. Having it for real changes how the signal lands.