A challenge faced by individuals and groups of many species is determining how resources and activities should be spatially distributed: centralized or decentralized. This distribution problem is hard to understand due to the many costs and benefits of each strategy in different settings. Ant colonies are faced by this problem and demonstrate two solutions: (1) Centralizing resources in a single nest (monodomy); and (2) Decentralizing by spreading resources across many nests (polydomy). Despite the possibilities for using this system to study the centralization/decentralization problem, the trade-offs associated with using either polydomy or monodomy are poorly understood due to a lack of empirical data and cohesive theory. Here, we present a dynamic network model of a population of ant nests which is based on observations of a facultatively polydomous ant species (Formica lugubris). We use the model to test several key hypotheses for costs and benefits of polydomy and monodomy and show that decentralization is advantageous when resource acquisition costs are high, nest size is limited, resources are clustered and there is a risk of nest destruction, but centralization prevails when resource availability fluctuates and nest size is limited. Our model explains the phylogenetic and ecological diversity of polydomous ants, demonstrates several trade-offs of decentralization and centralization, and provides testable predictions for empirical work on ants and in other systems.