Note: due to changes in the recently released 3.3, a lot of the guides may no longer be totally accurate. It will take months to reanalyse all the data and research the new behaviour.
What economical model is behind it and what are the limitations?
The economic model is quite abstract but can still give interesting behaviour. I have a rough summary at
https://forums.frontier.co.uk/showt...ets-supply-demand-and-relationship-to-the-BGS though a lot of the specific numbers are likely to have changed in 3.3
3307 a dictatorship dominates the entire universe? Possible in this model, not possible?
A single faction would only be able to spread to systems within expansion range, so it would need to hop no more than 40LY at a time. So it could dominate the main bubble and Pleiades [1], but not the deep space stations or some of the further out systems in the bubble's halo.
3307 would be too soon - the hard limiting factor is the speed at which a faction can expand to a system it's not yet present in, which is approximately one system every two weeks. That would therefore mean it would take around 750 years for a single faction to expand to be present in every reachable populated system, assuming no opposition and perfect management. But by 4307 it would be theoretically possible.
(That's for a single specific dictatorship. By 3307 assuming no opposition and perfect management it would certainly be possible to have every system in the primary bubble controlled by *a* dictatorship)
In practice of course other factions would have their own agendas and therefore would act against it. A single faction controlling 10 systems is large, a faction controlling 50 systems is extremely large.
What level of AI is perhaps involved in the BGS?
None, even by today's over-hyped standards of what counts as AI. It's all fairly simple at the micro-level, responding in various deterministic ways to player activity ... it's the emergent macro consequences of that which are complex.
[1] For an ultra-picky side point, there are also four key systems in the bubble which cannot be expanded into or taken over, so the faction would need to omit those.