Stability and Preference Alignment in Matching and Coalition Formation

We study frictionless matching and coalition formation environments. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences, we show that there exists a core stable coalition structure in every state of nature if, and only if, agents' preferences are pairwise-aligned in every state of nature. In particular, we establish that there is a stable coalition structure if agents' preferences are generated by Nash bargaining over coalitional outputs. Looking at all stability-inducing rules for sharing outputs, we show that all of them may be represented by a profile of agents' bargaining functions, and that agents match assortatively with respect to these bargaining functions. We thus show that assortativeness is inherently related to stability, rather than being driven by particular modeling choices of agents' sharing of output. The framework allows us to show that the presence of complementarities and peer effects – two important phenomena whose analysis was missing from prior theoretical work on matching – overturns some of the well-known comparative statics of many-to-one matching