Game, has a bad sound to it when describing a relationship. If you clean it up with politically correct type words you might say I should be more proactive instead of always being reactive.
I would not use the word "game" (unless your a student of transactional analysis) in even talking to myself - it is marginalizing her in your own mind and that isn't going to help.
She has a skills deficit. She is not outwitting you.
So lately I heard this new phrase "we would not be having the problems we are having now if you loved me"
I might suggest modifying your approach a little... .sit down after the fact when things are calm and ask her to explain what she means and listen without and JADE. Let he be totally heard. Ask questions for her to get it all out.
Then write it down and show it to her. Tell her you need time to think about it.
Come back and discuss it later in a time of calm... .don't JADE hear either, just get all her solutions expressed. Tell her you need time to think about it.
And then come back with some ideas... .
If its a cyclical problem, as it often is, it works to break it down this way.
She probably really thinks this and feels you are not listening... .whether that seems right or not to you... .and it will help to listen.
When you get there, it would be a good time to strategize here on how to deal with this problem.