A sad negotiation game

This morning as my wife and I were leaving for church, there was an altercation in the street outside of our house. A woman was walking down the side of the street and was being harassed by a woman driving a car. I pulled along the lady that was walking and asked if she needed help. She said no. But it was clear she was afraid. So, I stayed and watched. At least to deter any physical encounters between the two. The lady in the car, kept harassing the other lady, and she finally came over to me and asked for help. During this time, the lady in the car was saying unfriendly things to me and making unfriendly gestures. I called the police. They came and difused the situation.

While the police were there, the aggressor lady yelled at the other lady and asked, "do you want to work this out or do you want this?" indicating the police. At that point, it dawned on me, this has the elements of a negotiation game.

This started as a 2-party negotiation between "A" the lady walking and "E" the agressor in the car. As long as this was a 2-party negotiation, A was at a disadvantage and would continue to be harassed by E. Once my wife and I entered, the negotiation changed, mainly because E lost credibility in some of her threats, such as violence. A also now had a potential strategy of leaving the negotiation. As it happened, E took A's phone, so she had no way to communicate to friends or family. Once the police came, the negotiation changed again, and E had no power. A was then free to leave the negotiation.

When E asked if A wanted to work this out, she was actually trying to return the negotiation back to a 2-party effort, where she clearly had the upper hand.

My wife and I gave A a ride to her mothers. I don't know if she will choose to remain away from the negotiation or not, it is her choice. That being said, I saw game theory where I didn't expect it, in a hostile, domestic dispute.