A stable competitive market never has more than three significant competitors, the largest of which has no more than four times the market share of the smallest.
The conditions which create this rule are:
A ratio of 2 to 1 in market share between any two competitors seems to be the equilibrium point at which it is neither practical nor advantageous for either competitor to increase or decrease share. This is an empirical observation.
Any competitor with less than one quarter the share of the largest competitor cannot be an effective competitor. This too is empirical but is predictable from experience curve relationships.
Characteristically, this should eventually lead to a market share ranking of each competitor one half that of the next larger competitor with the smallest no less than one quarter the largest. Mathematically, it is impossible to meet both conditions with more than three competitors.
The Rule of Three and Four is a hypothesis. It is not subject to rigorous proof. It does seem to match well observable facts in fields as diverse as steam turbines, automobiles, baby food, soft drinks and airplanes. If even approximately true, the implications are important.
The underlying logic is straightforward. Cost is a function of market share as a result of the experience curve effect.