Complementarities of preferences have been known to jeopardize the stability of two-sided matching, yet they are a pervasive feature of many markets. We revisit the stability issue with such preferences in a large market.
Workers have preferences over firms while firms have preferences over distributions of workers and may exhibit complementarity. We demonstrate that if each firm's choice changes continuously as the set of available workers changes, then there exists a stable matching even with complementarity. Building on this result, we show that
there exists an approximately stable matching in any large finite economy. We extend our framework to accommodate indifferences in firms' preferences, construct a stable mechanism that is strategy-proof and equitable for workers perceived as indifferent by firms, and apply the analysis to probabilistic and time-share matching models with a finite number of firms and workers.