If the environment is sufficiently stable to allow the beneficial effects of side-effect shielding to continue, then:
Systems of large numbers of control units tend to self-organize into modular structures.
Although the structure may initially conflict or inadvertently disturb one another, "reorganization" brings their relationship into a configuration in which they largely support one anothe. These configurations are marginally stable. When confronted with novel influences such as the presence of a new module, they may be destroyed, change radically, or change only subtly.
Changes in one module may induce changes in its neighbours, creating the likelihood of "sandpile avalanches," in which the magnitude of change is totally unpredictable. But after a change, of whatever magnitude, eithe the systems will have been destroyed or a new organization will have been created, in which cooperation, not competition, is dominant.
Cooperation and conflict are inherent in Powers' insight that "All behaviour is the control of perception."
But in the end, cooperation will win over competition.
[Note added subsequently: This conclusion is too optimistic, since an undisturbed complex system can have other attractors than a fixed point. Other attractors might be oscillators or strange. In either case, the system as a whole keeps changing.
More to the point, systems that evolve through the kind of reorganization discussed here tend toward "the edge of chaos", a state in which transient disturbances may take indefinitely long to die out, even though the theoretical attractor might be a fixed point. So, even though cooperation is very likely to win in the end, nevertheless, "in the end" could be longer than the lifetime of a civilization, and any novel disturbance such as climate change could induce a new transient of indefinite duration.]