I got a message that a fight had broken out in Mother Base. I was at the Base at the time and couldn't see any signs of scuffle nearby, but didn't bother to check the other platforms. What does the fight mean, why does it happen, what should I do about it and what happens if I don't?
When the game notifies you that a fight took place at Mother Base it essentially means that one soldier with the Troublemaker (Violence) trait (that you can view from the Staff Management in the game menu by hovering over the soldier) got into a fight and sent another staff member and ultimately injured them.
To prevent future incidents you have a couple of options the first one is to remove any staff with the trait Troublemaker (Violence) from the organization. Usually this is a good idea for low-ranking soldiers (all skills C or below) but suppose you have a high skilled soldier that happens to have that trait.
Secondly, you can assign another person with the same Troublemaker (Violence) trait in the same skill group. Because there will be two or more Troublemakers with the same trait then they will keep each other on watch, and no fights will actually break out.
Finally, you can also use a staff member with the Diplomat skill. They will help preventing fights from breaking out at Mother Base.
On the other hand this doesn't apply for Troublemaker (Unsanitary); they can be negated since the other Troublemaker with the same trait will negate the effect, but it also depends on your Medical team's effectiveness.
These events cannot be seen take place real-time at Mother Base. My guess is that they are there to encourage you to regularly keep an eye on the staff.
I don't think those actually happen in the game world for you to stop.
They are caused by the ability 'Troublemaker' on one of your people, the chance they will start something can be lowered by the ability 'Diplomat'
People also seem to be having them stop hurting others if there is another 'Troublemaker' I haven't experienced this as I fire them