The first major issue people faced in these areas was the problem of how to sustain a food supply. The neolithic transition, in which people settled down in one area to farm rather than moving as hunter-gatherers, allowed for more efficient food production than had existed previously, but the increased population density also required the ability to produce a steady food supply within a limited area. In both regions, this required people to cooperate to develop irrigation systems.
The concentration of population in fixed settlements raises other issues that would not have been problems in small bands of hunter-gatherers. One needs to arrange for clean drinking water and disposal of human waste downstream of sources of drinking water, for example. The use of fire for cooking and metallurgy in a settlement means one needs a cooperative means of dealing with fires. As one no longer has the safety valve of forming a new small band and moving away from conflicts, there needs to be some official conflict resolution mechanism and various forms of laws about property. All these give rise to the need for many of the mechanisms of government that we see developing in ancient Egypt and Mesopotamia, including legal codes, taxation, and some form of government bureaucracy.