The dissolution into tribal organization was not a descent into anarchy. The tribes, or kinship groups, already had an internal organizational structure that had functioned within the larger government. Removing the larger governmental structure did not remove government entirely, only the recognition of a government that united them. In the division into tribes the different peoples occupied different lands and set about the task of providing.
It was certainly in their best interests to decrease the threats of warfare, as warfare took time and resources. With the reduction of the governmental organization, there was also a reduction in the available surplus, and each of the communities needed to regroup and supply their own needs. It was in their best interests to be peaceful and to take care of the business of providing for their own.