This is an interesting (if somewhat morbid) thought experiment. Personally, I think that at least some people will fight each other. Dying is not a pre-requisite for conflict. If two groups of people hold strong beliefs and/or opposing opinions on a highly controversial issue, conflict will arise and with conflict can come violence. It is of course not always rational sometimes, people just don't do the most rational thing for a myriad of different reasons. It's part of being human. The chances of conflict rises exponentially in your scenario since they are being held here against their will. That alone is enough to spark tensions and if the people hold strong and/or opposing beliefs, conflict will be pretty much inevitable.

As for how they would fight, that depends on their personal beliefs. Some might believe in honourable duels where the fight continues until one side is unambiguously the victor. However, they might also fight