Please do. Most of the time, anti-trust laws favor the start up bringing the complaint over the big, established company. Right now the laws are not being enforced very well and have not been enforced very well for 30 years (you can basically get away with restraints of trade right now).
Restraints of trade create monopolies and stifle competition. There is a very complicated formula for looking at this. Basically, under current laws if they were being enforced, you can restrain trade as long as you have a low market share and the effects of your restraint are not enough to influence the market. Apple and those phone companies (AT&T, etc) have a great percentage of the market share and their restraints certiainly create barriers for entry and allow them control over the market. If there are significant barriers to entry being controlled a few large companies, there can be no perfect competition, there is no free market and everything is kaput.
Sherman Antitrust Act 1890--forbids anyone to monopolize or attempt to monopolize or engage in restraint of trade
Clayton Act 1914 and Federal Trade Commission Act both 1914)-forbids acts incidental to monopolization such as restraint of trade and various unfair business practices
Robinson Patman Act 1936 and Celler Amendment 1950-more regulation against price discrimination, obstacles to firms wanting to merge
The problem with these laws is exhibited in your post. You state that "there is a very complicated formula for looking at this". The reason the formula is so complicated is because there is a wide variance in
definitions, and the formulae allow discretion by the administrators. What may be a significant barrier of entry to you is probably going to be different for someone else. The guidelines used are also subjective, ridiculous ways to estimate competition post-mergers. Just reading the "Upward Pricing Pressure" guidelines and HHI is a waste of valuable time.
What someone may define as a particular product may lump together a number of products that have divergent characteristics. Mobile phones are a good example of the "definition" problem. For example, you state Apple and "those phone companies" have control over the market. This is not correct. Samsung, HTC, Google, Motorola, Sony and LG sell phones, and there are many carriers (Verizon, Boost, Cricket, Net10, H2O, T-Mobile, Cricket etc.).
Another issue is substitutability of products. If you were to buy every typewriter company in the world, you would have a monopoly by most common definitions. Theoretically, you would raise your typewriter prices above the level that you could in the face of competition. However, no one is going to buy the typewriters at an unusually high price because substitutes are available in the form of computers and printers. Also, just owning all of the companies does not prevent someone else from starting a typewriter company. Life Magazine was a dominant firm at one time. In my freshman year at Texas, we used punch cards that ran through "computers" to perform basic calculations. By the time I graduated, there were desktop personal computers available. There may have been a monopoly on punch cards at one time, but three years later that was irrelevant.
The next problem is illustrated in your post also. You have gone from defining "monopoly" (where one company produces all output) to calling a monopoly "a few large companies". The "few large companies" are known as "competitors". The definition of a true monopoly is the ability to
prevent competitors from doing the same thing. Those companies rarely exist without government interference.
If two companies control 75% of the market, but there are 40 competitors that have the remaining 25%, the two large companies haven't prevented others from competing.
What is lost is the ability to examine companies based on efficiency, innovation, product quality, marketing, etc. inherent within various firms. How about management ability? Where does that come into play? Why should management teams be held equal when examining markets?
The Robinson Patman act was said to prevent price discrimination that reduced competition. Its evolution was due to large retail chains buying huge quantities and selling at prices that were
lower than local merchants. The same complaint is often lodged against Walmart today. Antitrust cases were brought against Great Northern Railroad and Standard Oil Company, which were companies that charged lower prices than their competitors. See Anheuser Busch v FTC where action was brought because the beer company was selling beer at a
lower price in St. Louis. In FTC v Morton Salt, Morton was prosecuted for selling salt to those purchasers buying in boxcar loads at a price lower than to those buying in small quantities. In the opinion, the following is stated:
The legislative history of the Robinson-Patman Act makes it abundantly clear that Congress considered it to be an evil that a large buyer could secure a competitive advantage over a small buyer solely because of the large buyer's quantity purchasing ability. There are many, many examples of the government prosecuting firms for selling products at a price lower than the competition.