What eventually happened was that refinery producers began building refineries just so they could sell them to Rockefeller because they knew he would buy them.

Rockefeller eventually realized that he couldn’t keep buying all the oil refineries because he would bankrupt himself since people would simply keep building them until he ran out of money.

Obviously the lesson to be learned here is that it is impossible for any single corporation to buy up all the productive capacity of a given market because people will keep building more production facilities until the monopolist stops buying them or is driven into bankruptcy.

So my whole point here is that a monopolist does not necessarily have to be a stupid idiot bastard, basing his profits solely on evil and unethical behavior. He can be smart and adaptive as well, even bowing his head to the market to some extent, but still use all his available resources and advantage to always keep at least a step ahead of all and any of his rivals that might emerge. So while this is not a monopoly in the classic sense as described above, but in its effects, it would be quite similar.

Remember, the whole point behind having monopolies stopped is that they are bad for the consumer, and result in higher prices.

That is – furthering your example -, another thing I could – and what in this case I would – do as the monopolist is – instead of cutting production and driving up price – to just max production and meet the demand, since even if the prices are lower, due to huge amount produced, I’ll still make a fortune – possibly even more than I could with higher prices but smaller quantity.
And if you still come along to compete, well, I just buy you out. Since there is no authority to tell me that I cannot, I will. And if you don’t want to sell your business, then I don’t even have to cheat – I can just simply let you try, confident in my superiority (since I’ve already maxed production, the prices are low, and you can’t bid under them, because you have only a small startup production facility, while I have many factories throughout the planet, and can produce much more a lot cheaply and with better quality than you), knowing that you are going to fail anyway.

So that was my theory – but now I see that this apparently does not count as a _real_ monopoly, since in this case competition is still possible… with low starting chances, but still possible. I see. Thanks again for the answer!

Why would a monopolist expect to get away with “cheating” (you don’t say what sort of cheating) easier under anarcho-capitalism than under the State?  Do you have ANY evidence that the state is actually good at being a referee or preventing cheating?  Because there is a lot of evidence that it’s rubbish at that.  About 100 million pieces of evidence, all of them dead bodies.