One such set of Program A and Program B is 'attached' to every individual in the world. Being of equal intelligence, in THEORY they should compromise in order to avoid wasting resources.

Ecosystems of many cooperating agents only work so long as either they all have similar goals, or there is a suitable balance between offense and defense. This particular example fails if there is any one person in the world who wants to destroy it, because their AI can achieve this goal without having to compromise or communicate with any of the others.