Logic Beasts

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Anyone know those recursive logic puzzles like the one with the hats and the one with the eyes, were they make really convoluted conclusions based on how the others would solve those problems? I find their conclusions to not really be logical at all, because they make extremely unrealistic assumptions about how people behave. So in order for the puzzles to work as intended, the participants need to not be human, but Logic Beasts. Logic Beasts seem to have three core characteristics:

1. They are logically perfect. This means that if there is some collections of statements which only has one satisfying configuration with some collection of premises, they know what that configuration is. By extension, they also know if they lack sufficient information to make a conclusion.

2. They are deterministic. This means that they will always act in the same way given the same information.

3. They are self-aware. This means they know how they (and other Logic Beasts) would act given certain information.

The problem comes from precisely defining exactly how a logic beast would act for a particular problem, which is vital for the self-aware criterion. The most precise model for deterministic behavior is a robot. However, it's impossible for a robot to also be logically perfect, due to the existence of unrecognizable languages which are still well-defined logically. So does anyone know a good model for such logical beasts?

I've concluded all three lead to a contradiction. Imagine you had two logic beasts playing rock-paper-scissors against each other, and they play to win. If they are deterministic, they'll always throw the same sign. Since they are self-aware and logically perfect, they'll know what the other is going to throw and can throw the counter. But they can't, because then it would not longer when because the other would throw something different. So logically they can't throw anything.