The game of cat and mouse that Lily and Selden are playing is a little annoying. No one wants to bend and yet they are both expecting the other to give in if their relationship is going to take off. Even though I feel as if Selden only applies this to his courtship of Lily, Lily on the other hand plays cat and mouse with her status in her society. She gambles when it is not proper for her to do so, she smokes when it is not proper for her to do so, and she doesn't have the money to maintain her expensive appearance. Lily is way to stubborn to submit to all the rules that tells her what she should do, she does what she wants to do.
There are times where it appears she is going to go beyond her stubbornness, but in the end goes back to her old ways. The first example of this is in the train car where she attempts to hide who she is in an attempt to court Mr. Gryce. She attempts to hide the fact that she smokes and engages him in conversation with him regarding the things that he likes, but she doesn't have any genuine interest in them. Later in the novel Mr. Gryce proposes to her, but she declines. I feel she declines because of the stubbornness of not wanting to change who she is if she were to marry him.