One of the core objectives of social science in general, and of archaeology in particular, is to explain the emergence and development of complex social systems-i.e., social systems with status inequality and government by non-kin-based authority. In this chapter, we implement an empirically calibrated, spatial agent-based model (ABM) as a tool for studying why and how wealth differentials and associated social inequalities are generated and sustained over multiple generations. We also describe the theoretical foundation, formal strategies, and examples of the mathematical and computational approaches needed to develop complex ABMs.