Let’s say we have N players. The first consequence would be the existence of a unique price.
That’s not true if one of the players has a monopoly.
A monopoly will extract as much as it can, delivering as little as possible.
It will be able to charge different prices from different customers. In a free and unregulated market, the monopoly can award you (“prime” customer!) or punish you—it is the lawmaker, juror and executioner.
At this point, everyone will specialize in one good (banana or coconut) based on whether each one values banana/coconut more or less than the market does.
This scenario is not supported by reality.
What we see, in practice, is that free, unregulated market will create monopolies.
As small companies compete, you naturally get market leaders. As these companies get larger they become more efficient at producing goods and services. They invest in mass production techniques in order to produce goods more cheaply than their competitors. They buy raw materials at cheaper prices because they buy in bulk. They expand specialization amongst their workforce. The bigger they get, the easier it is to make money. Smaller companies cannot compete.
When two market leaders merge they achieve massive economies of scale. This forces others to merge in order to compete, leading to ever greater concentration. Monopolies often buy their rivals.
The only solution to this is to admit that we need regulation and laws.
There is no such thing as “free and unregulated” market. An unregulated market will not be free.