This has not been shown. This is repeatedly conjectured (no evidence) by the fine people at mises.org. Also, companies don't actually like competition, which is why they spend so much time and money trying to distort markets. So the conditions for which foster this fabled competition don't even exist. They definitely won't exist if it is up to them. So this argument, which is critical for everything else that supposedly follows, falls pathetically flat.
.
Competition is the best weapon for combating abuses by private powers. Look at the cellular industry. Google dragged cellular network providers kicking and screaming to providing better plans to android users. It's not impossible to bring competition in this skewed environment as google have shown.
It will be a lot easier to introduce competition in an environment where corporations will borne the cost of warring by themselves and where privilege and monopoly are not as widespread.
This is how agorists(I am NOT one because I am a chicken) combat abuses, by counter-economic revolutionary activities.