If they are allowed to build weapons, there will be war (for resources / power)

Thats a definite result.

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AI:
What you basically want to do is an artificial-life simulation?
If the actor a supposed to be "concious" (can learn / plan)
it will get very complex.
If they act rather static (such as suing a finite state machine)
it should be doable.

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test: if world with no money could exist.

You can have a world, but I think you mean an economy.
When money was not available in eraly economies, people
used the bartering system (x-apples for y-leather)

Money simply makes trading much more efficient, faster
and fair (only prices have to be remembered, not relative
values of two item groups)