Yes they do have a pecking order. I used to feed my two frogs together and one of them would eat all of the crickets, while the other ate none. I thought it wasn't hungry until I saw it go for a cricket before the other one was finished eating, and the other one jumped and bit at the frog. Now I feed them in separate tanks but put them together in between.
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No, tigers are largely solitary hunters.
The only time they live in groups is a female with young, but once she has trained them to hunt she abandons them and they must live individually.