There are two main ways of running a game in the Anarchy Zone setting, and. these styles are mirrored opposites of each other. Internal games focus on the population of a single city state, while the outside is on the areas outside.
Internal games are usually fairly close to the standard zombie apocalypse scenario. Beyond the walls of your home settlement or city state, is a wasteland full of things that want to eat you, and human scum that is probably worse. Instead, you must build alliances amongst your fellow survivors, quell the rumbles of unrest, and try to rebuild as best as possible.
Sometimes this involves investigating a murderer when the culprit is hiding in the miles of NEST maintainece halls. Other times its helping lead the rebellion against the Birmingham Theocracy, only to turn on your so called comrades and show you were an Inquisitor and in the right all along. Considering that many of the city states have been running under absolute authority for several years now, just getting elections to run smoothly could involve risking your life and protecting others at the polls.
It may be necessary to leave the walls and find some supply to help with the long term survival of the state. If its possible to make someone else go, all the better.
External games are about exploration and freedom, dodging reanimates along the way. There are places with a population of several thousand, running water, and restored sphere access. However, they are merely grasping at the former grandeur, and maintaining them through draconian measures. Leaders are willing to exile or execute anyone who doesn't wave the tattered old flag of nationalism. Every last one of those residents is willing to kill their bretheren to keep just a little more of the bones of the past to themselves.
Games on the external model focus more on the beauty and opportunities of the anarchy zones. This is a time for pioneers, not all that worse than the nineteenth century. Aliens have replaced cholera, reanimates indians, and a nano tech factory is the new comstock lode. Make your own legend in the wastes, and help others along the way if you can. With a sudden population crash, an invasion wiping out old nations, its a chance to have the world new again - there is space and resources enugh for everyone if they put a little work into it.