In the economic sense of the term, competition refers to the incentive to better appease a multiplicity of demands, and cooperation refers to the most efficient and ethical means of meeting such demands. An individual's demands are better met through cooperation and production than through isolation and destruction. Competition does not refer to a war of all against all or atomism, it refers to a process in which decentralised cooperation is employed in the attempt to fulfil a dynamic and variant latticework of demands. Monopoly, on the other hand, refers to the lack of competition, the imposition of a singular or more limited array of options through coercive means. Competition and monopoly are therefore dichotomous in this sense, as competition entails a multiplicity of options pursued freely. Competition is a reflection of there being multiple methods of cooperation and multiple ends that cooperation can be used to pursue, and as such there is no absolute dichotomy between competition and cooperation.
Individualism does not regard the individual as if they exist in a vacuum, it merely recognises the individual's sovereignty as co-existing with interpersonal relations, and that it is a fundamental building block of a society. It is erroneous to present a false dichotomy between uniformity and atomism, when neither of the two reflect the nature of an individual let alone a society. Society qua society is founded on voluntary cooperation, but this does not conflict with individual sovereignty. Voluntary cooperation is merely the net effect of people making use of their individual sovereignty, and competition is merely a reflection of the diversity of wants that people pursue as sovereigns. While interpersonal relations are something to take into account, the individual still retains their independence from the transgressions of others in an equilibrium, which acknowledges the competitive element of society that is responsible for creativity and innovation.
Cooperation and production is not an ethical imperative in and of itself, it is something that one has a greater incentive towards in conditions of equal liberty. However, one ultimately retains their sovereignty to not produce and not participate in a particular organisation or interaction that they didn't explicitly consent to. In a voluntary society, the methods in which one cooperates and the extent to which there is a binding obligation to cooperate can only be in a contractual context in which consent is explicitly given prior to the enforcement of the obligation. One does not have an unchosen positive obligation to be a member of a particular organisation or to participate in its process of decision-making. The implication of this is not the negation of society as such, but the decentralisation of society as a consequence of people entering and exiting from a wide array of contractual agreements.
The coercive imposition of uniformity stifles cooperation. It disincentivises and erodes at competitive alternatives that otherwise would have been fostered through cooperation, and it violates the individual's sovereignty. Coercion is anti-cooperative by its very nature, as it can only establish a parasitic relationship or a zero sum game, while cooperation is geared towards mutual benefit or reciprocal relationships. Centralisation and monopoly can only establish the elimination of individual choice in the process of cooperation, and therefore the elimination of competition. Competition is necessary to counteract the arbitrary imposition of a particular set of preferences, otherwise there is no genuine cooperation to speak of, only subservience. Cooperation is not something that is centrally planned or coercively enforced, it is a process of spontaneous order.