Dogs are pack animals and they decide who is top dog. Hopefully the people in their lives will fill the top dog space, but they will vy for second, third, fourth position within the pack. I'm sure this is what they are establishing and once established it will determine who sleeps in an elevated spot ( higher in the pecking order) and who eats first, etc. It is best not to interfere except to let them know that you get the bed, they sleep on a lower surface than you, maybe the floor, but definitely at the bottom of the bed and not at your head, you eat first and never feed them from the table. If they are fighting for food or if one gets a majority of the food not letting the other one eat, feed them in separate dishes or at separate times. The key is to let them establish who is highest in order.
Thurid Rugaas has writtena good book; On Talking Terms With Dogs; Calming Signals. You may find this book helpful. I bought a copy on Amazon new for around $6 and it was a quick read of only a few hours. It may be worth the price to understand your dogs and even communicate with them better.