Most US States have laws regarding domestic violence that can be applied to these situations. Assuming someone calls the police, the officers are empowered to arrest either or both parties where they observe any sign of physical injury on the other person, despite their lack of witnessing the altercation, and despite the lack of either party making a complaint against the other. In short, they can arrest both parties on presumptive assault and battery, if injuries are observed, and let the court sort out what happened, and what to do about it. It may be that the prosecutor decides to drop the charges, but you will first be arrested, arraigned, charged, bailed and must eventually defend and explain. Probably you will also incur legal fees and could end up with a record of some kind.
In every State in the US, it is ILLEGAL and against public policy to make a contract for the commission of a crime (assault, battery, etc., being statutory crimes). Any such contract is probably unenforceable at law or in equity. Most states have a set of statutes that apply to the regulation of "prize fighting." One may be able to utilize compliance with those laws to escape criminal prosecution. That said, they are often very expensive and tedious to comply with.