On the Equilibrium Properties of Spatial Models

We consider a broad class of spatial models where there are many types of interactions across a large number of locations. We provide a new theorem that offers an iterative algorithm for calculating an equilibrium and sufficient and "globally necessary" conditions under which the equilibrium is unique. We show how this theorem enables the characterization of equilibrium properties for one important spatial system: an urban model with spillovers across a large number of different types of agents. An online appendix provides 12 additional examples of both spatial and nonspatial economic frameworks for which our theorem provides new equilibrium characterizations.