These imaginary tycoons of yours must have endlessly deep pockets to be able to sustain such control. What exactly is the scenario here? The tycoon is forking out loads of cash to monopolize a security agency, and all competitors, and the passive masses continue to fund him so that he can oppress them via third party?
Of course, ideally there'd be no State, and thus the volatile market absent corporatism, coercive monopolization, barriers to entry, and other State interventions of this nature, on top of a rearmament of the citizenry, would make this whole hypothetical virtually impossible as far as I can tell. This is not to say that there wouldn't be a time needed for market experimentation and such, but it tends to be pretty good at satisfying demands even under such an interventionist State as we have now, so I can only assume its levels of efficiency and productivity, as well as its ability to satisfy demand would dramatically increase absent the State.
The real problem would be foreign States propping up dictators and warlords, like the US has been doing for decades. Then again, they might ultimately end up fucking themselves over a la USSR.