In classical economics its obvious that the philosophical model followed is inspired by both physics in its reductionism and biology to a primary notion - that of self-interest. This self-interest manifests itself in competition. So we may as well take here competition as the basic notion.
Cooperation as in cartels, or in a trade union is explained as altruism is in biology by reference to competition. The members of the trade union for example may find that their best interests are served by cooperating. So here cooperation is explained in terms of self-interest or competition. That is they find that the best way to compete is by cooperating.
Is there an economic philosophy that takes both cooperation & competition to be irreducible to each other? An example of competition that can be explained in terms of cooperation is a game of poker the players must cooperate to play before the begin to compete. A company before it can trade must abide by laws and regulations or at least be seen to do so. That is it is cooperating with what one can say is government - that is the body or bodies that are concerned with enacting laws that hold over all society.
One could say that classical economic theory is monistic whereas I'm asking for a dualistic one. These are of course philosophical, theological & ethical terms - I do not know whether they have been used in the philosophy of economics before.