If any market is simply left to its own devices, what happens is firms begin to either consolidate or drive out rival competitors. They also begin to erect barriers to entry to prevent new firms from entering the market.
When competition whittles down to simply a few or two competitors and then eventually to one, a monopoly is achieved, and the game ends. In real life, though, people demanded change to the point where politicians finally passed the Sherman Anti-Trust Act of 1890, the first of several laws aimed at destroying monopolies and preventing unfair competition and business practices.
The only thing I would add is that I believe oligopolies can be just as dangerous as a true monopoly. In an oligopoly, only a small number of firms exist in a particular market, and competition between these few firms is very light because the few actors in this market realized that competition itself was destructive, that it would be in their mutual best interest not to compete on price, to coordinate in the raising of prices for everybody's benefit. Of course, it doesn't benefit the consumer. Incidentally, this is why health insurance premiums are rising faster than the wages of most people: Lack of competition.
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