Animals living in packs must have ways to decide how to distribute their goods among the pack members. Just like prices can appear in an exchange economy, prices could appear in pack economy. Though money can serve many different functions, are there examples of money-like objects (abstract symbols of value?) in the animal kingdom?
The only use of money (other than by humans— who, it should be noted, lived for most of human history without it) in the animal kingdom that I'm aware of has been when researchers have taught other primates (Capuchin monkeys) how to use it. While the introduction of currency was apparently successful (there was Capuchin prostitution), the research did not go so far as to show that equilibrium prices would arise endogenously through exchange.
This might not exactly get at the get of situations you are interested in, but you might be interested in the famous "Fairness-study" on capuchin monkeys. You can find a quick account of the study in this video
Of course, this is a lab, not strictly speaking in a natural environment. Also, there is no trade through money between monkeys themselves, only something that resembles monetary trading between the monkeys and the experimenters.
Maybe this only suggests that monkeys potentially have the ability of engaging into monetary trading? But that might be taking the results of the experiment a little too far.
Consider a standard exchange economy (agents are endowed with some set of goods that they will use to trade with others). Piccione and Rubenstein wrote a somewhat interesting paper about "jungle equilibria" of an exchange economy.
In their paper, allocations are decided by allowing more powerful animals are able to take goods from weaker animals (I don't think their preferences were necessarily monotonic -- i.e. I think there was satiation). They not only show that an equilibrium of this form exists, but that it is Pareto efficient (you can't make anyone better off without making someone else worse off).
Obviously this paper isn't exactly a model of the jungle, but the point is that there could be an equilibrium in the wild which follows a framework similar to this (and I think it is a cool paper and your question reminded me of it).