If I'm farming mobs, and another player starts killing them, I just reduce my farming radius. Most will see what I'm doing, and just farm what I'm leaving alone. For those who don't, I try to nicely work it out with them via chat. If I'm ignored, I just wait for them to finish, or I move on.

I ran up on my favorite fleece spot yesterday, only to find another character there. They appeared to be prepping to farm them, so I asked if they were doing so via /say. They replied that they were done, and to go ahead. I thanked them, and got to work. Communication has made farming much easier more times than I can count...

I never try to compete for mobs, because I consider it a waste of time. There is plenty else to do without resorting to competition without reward.