Mouse with Wound on Tail

Hey all-

I have a pair of male mice and have had them for about 5 months. Recently, maybe 3 weeks ago, I've notice there were dominance issues and territory issues as well. The "alpha" mouse would chase the other mouse around, bite at it's tail, would take food from it, chase it out of it's corner of the world.

I noticed today when giving them fresh food the non alpha had bite wounds and scrapes on the base of his tail. His genitals are alright, but I am wondering, can I use a weak solution of benadine on it? I've heard not to use neosporin cause they'll ingest.

Any ideas?

Oh I did seperate them. They each have their own cage, wheel, etc.

You can use betadine, however if it is a minor would he should heal just fine on it's own even without it.

Ok, thanks Deborah. It does seem very minor and already a few days old. I just wanted to be sure it was something I could do.