This paper develops a theory of competitive equilibrium with indivisible goods based entirely on economic conditions on demand. The key idea is to analyze complementarity and substitutability between bundles of goods, rather than merely between goods themselves. This approach allows us to formulate sufficient and essentially necessary conditions for equilibrium existence—which unify settings with complements and settings with substitutes. Our analysis has implications for auction design.

Current refugee resettlement processes account for neither the preferences of refugees nor the priorities of hosting communities. We introduce a new framework for matching with multidimensional knapsack constraints that captures the (possibly multidimensional) sizes of refugee families and the capacities of communities. We propose four refugee resettlement mechanisms and two solution concepts that can be used in refugee resettlement matching under various institutional and informational constraints. Our theoretical results and simulations using refugee resettlement data suggest that preference-based matching mechanisms can improve match efficiency, respect priorities of communities, and incentivize refugees to report where they would prefer to settle.