Where market competition exists it's effective in limiting prices and spurring innovation. But the natural tendency of successful businesses is to minimize exposure to competition. That can happen by buying the competition even if there's no state. (You can argue that regulatory capture is how successful businesses minimize competition by using the state, and I'm sympathetic to that argument, but it's also just another example of the tendency to eschew competition.)

OPEC is frequently divided against itself in terms of production targets; ExxonMobil is not. In a world without states there's no antitrust regulation preventing ExxonMobil from acquiring a market share equivalent to present OPEC, then exercising that pricing power with more effective discipline.

I am picturing the elimination of the state. And I agree that one can enforce his own property rights.

An entity that answers to no higher authority and enforces its own territorial claims with force is a de facto state. I understand and sympathize with many arguments for personal liberty over the power of the state. I don't understand the implication that unbounded private power is more trustworthy. It's an affront to liberty for the State of Delaware to exist and enforce its laws at the point of a gun, but it's ok if a corporation or family can acquire a Delaware-sized, Delaware-shaped parcel of land and enforce its decrees at gunpoint within those borders? That may not fairly represent your point of view. I have previously had arguments where self-proclaimed anarchocapitalists affirmed that it's fine for a small group of people to wield power equivalent to a state government as long as it's not called a state.