There is a simple thought experiment called the trolley problem. I will expand and make it darker and bloodier.
I suppose that you know the trolley problem and devotedly follow trolley problem memes. But to be sure: The wild trolley is heading to a crossing. You are next to a switch that can send the trolley to a second track. On the original one, five people are tied. They die if you don't flip the switch. If you do, only one person dies on the second track.
The moral dilemma is: kill one person to save five. Most people would flip the switch. One stranger is more than five.
One way to convince people not to kill is to make the one person a relative or a partner.
Interestingly, there is different phrasing that decreases the willingness to "kill one to save five". It's called the fat man problem. The story is the same: the runaway trolley is about to kill five people. Only you can stop it by pushing a fat man to the tracks.
It moral psychology showed that people evaluate the classical clean problem differently than this personal one. Flipping a switch makes the people act "rational". The idea of struggling with someone activates empathy centers.
But let's examine more complicated problems.
In the trolley problem, you can expect a person to act as he said he would. It might be different if the person is under pressure or invested in the outcome.
You and one another person are trapped in a cave (probably by an evil wizard). Only one person can leave the cave. After he leaves, the other person dies immediately. And everything left in the cave is destroyed (no evidence).
Now, this might reduce to a race towards the exit. That's not what the evil wizard wants, so if one person is willing and able, he can (by shouting) start flames around the exit that kill whoever is trying to escape.
Imagine the situation. You are sitting in front of one person. If you want to survive, you need to convince him to let you live or overpower him physically.
To make it more interesting, in the first round, you cannot touch. You can only talk. If a person concedes in the first round, he dies painlessly, and the other is free. If nobody wants to die, then it moves to the second round, where everything is allowed.
Should you even try to survive? In the first round, it seems fine. You can learn that the other is a mass murderer with intent to continue or mother of dependent children. But if you start fighting, you need to take the life of someone else to live.
Society views this victory as alright, with exceptions (children). If you are thinking about not fighting, you should fight. Then your strategy is easily exploitable by bad people.
What would be your arguments to convince someone to give up his life? It's probably not possible, but I would try to reason.
Some reasons that I would consider beneficial in the other person.
Harmful facts:
The question is whether we can trust the other person. I would not lie. It doesn't make sense.
Bargaining might be better than convincing someone about the worth of your life. I would personally follow any bargain if it makes sense, and I get something from that in the upcoming fight.
A perfect bargain is to take care of someone by paying survivor taxes (ten percent of your salary to family of the dead). Volunteering for some cause of the opponent's choice is also a great idea, so is honoring his legacy in any way.
If the contracts from the cave would be binding, it might decrease fighting and help rich people to survive. The contract with someone powerful might achieve more than you ever will. So if you have some aspiration (climate fight), someone else might do it better than you.
And what would convince you to give up your life?
Imagine you got with your opponent through the negotiation. No one conceded. It means a fight. But your opponent is more powerful: your survival probability is slim. Also, you have no deal.
Now, there are two possibilities. You can commit suicide or fight for death.
You should realize one thing. The other person is there unwillingly as you are. Killing someone might cause significant trauma. Not only that, but it might cause the person to be worse than he would otherwise be. So maybe you should commit suicide.
After you return from the cave, what would you tell happened? You can say whatever you want.
Would you do something to point out there was a contract or shrug it off? Or maybe you can say: we flipped a coin.
I imagine that the attacker has an advantage, so not to fight dirty is a losing strategy.
I would expect a dirty fight and also fight dirty. (Maybe it's wizard's experiment to tell how many pairs kill each other and nobody escape)
What if the wizard captures more people and only one can get out? I would behave as in the case with one person. The strategy is simple, ally against stronger people in the first phase. In the second phase, you overpower others, preferably do not break the agreements first.
But what if from all people one person cannot get out (or maybe a few people)? Then, dirty tricks are out of the table. There is someone to punish you. Probably people have similar values enough to agree on one person to kill. It would be easy. If it's not you, you will vote for anyone.
Maybe the cave problem would traumatize only modern people. In famines, wars, or polar expeditions, people faced similar dilemmas. Usually, it was not a clear cut as here, but in effect, a lot of people lived just because others have died.
Gladiators faced a similar dilemma, with one exception: there were spectators. It made the fight more "fair".
You survived. Does it change your life to know that you are living because someone else is dead?
In the beginning, it might create a change, but people will regress to the mean eventually.
I think that it's reasonable to fight unless you have an unbreakable contract. I would be willing to make contracts that give me no further chance for survival if my opponent does the same, like: whoever wins will pay the family some money or do something significant for the other. Also, I would honor that contract to the best of my abilities.