Yes, they must sort it out on their own to a degree, but you are also the Alpha and whatever you say goes. We had to seek experts when we got Millie and they both agreed that letting them sort it out totally on their own was a no-no. You are the Alpha and if you don't want any fights in your pack, then put your paw down.
We always have consequences if there's a disagreement. Take away the bones, put them both on a leash (yes, in the house), or no more playtime with toys or us. We had to control almost everything in the beginning. Chester is VERY dominant and used to be somewhat dog aggressive. As soon as we stopped letting them work it out, and took control of the situation, we've had a relatively pleasant two dog home.
Good Luck !