It's between 20 and 25 years ago that I read this hardback sci fi story. No cover details come to mind.
Story details: Generations earlier, mankind made it to part of the galaxy many light years away. There are a good number of star systems nearby and (I think) five or six alien races, all at a similar tech level to the humans.
Humanity managed to grab themselves a couple of habitable planets and join in with the interplanetary trading etc. I think they are long out of contact with Earth and are going it alone.
Occasionally there are disputes among the various races and they use a formalised combat to resolve any issues where diplomacy has failed. In one part of local space is a big old asteroid and this has been long since modified and is ran by an AI.
It has lots of concourses and tier upon tier of viewing galleries that look into a massive Ender's Game type battle arena. This is zero gravity and a selected number (20 maybe) of fighters from the rival races fight to the death inside it.
To allow for some species having a longer reach etc the weapons are all the same. A short stabbing blade affixed to the top of spacesuit helmets, therefore the attacker has to line up perfectly to get in a killing blow. The spacesuits have maneuvering jets.
In this story a cruiser from one alien world has seized a ship with some Terran girls on it, hostage negotiations then failed so Terran marines (I think) seize an equal number of alien girls and mankind issues a formal challenge.
There is some kind of error as the war parties, the hostages, diplomats, formal witnesses and frenzied mobs of gambling aliens all arrive at the neutral asteroid, somehow Earth is one girl hostage short (I can't remember why) so it looks like a proper space war will happen instead..
Suddenly salvation! A volunteer has came forward, news sources reveal her as a high-ranked Terran's daughter but also, and more importantly to him, she is the girlfriend of the hero of the combat team, now he and his men dare not lose or she will be slaughtered together with the other hostages.
There were several battle descriptions as the combatants killed one another but then lots of alarms sounded and the asteroid had to be evacuated. The hero and girl are prevented from evacuating by one thing and another and soon they're the only ones left.
The AI then fires up drive engines that nobody knew about and they're hurtling across the galaxy. It tells them humanity is too disruptive for the long term stability of the local Star systems so it's taking them to a fresh place to start again.
Without the neutral asteroid there will quickly be large wars behind them and most likely no humans left at the end.