If it were necessary to give the briefest possible definition of imperialism we should have to say that imperialism is the monopoly stage of capitalism. Such a definition would include what is most important, for, on the one hand, finance capital is the bank capital of a few very big monopolist banks, merged with the capital of the monopolist associations of industrialists; and, on the other hand, the division of the world is the transition from a colonial policy which has extended without hindrance to territories unseized by any capitalist power, to a colonial policy of monopolist possession of the territory of the world, which has been completely divided up.
That's...not really true in any substantive sense. Capitalist imperialism co-developed with capitalism the whole time the latter was developing from pre-capitalist systems. The only way you can say either came later is if you artificially construct both as binary rather than continuous transitions and then draw the arbitrary binary line one each to make that ordering work.
Every-man-for-himself type situations can also foster savage competition. Individuals can be savagely competitive.
Capital rather enables anti-competition: eliminating the need to compete by eradicating competitors through monopolistic power, and gentlemen's agreements regarding pricing and territory.
Whenever two people pool their resources together to form the capital base for a business venture, they cease to be potential competitors. From that alone we can suspect that capitalism is more about savage accretion and acquisition rather than competition.