Pairwise stable matching in large economies

We formulate a general model and stability notion for two-sided pairwise matching problems with individually insignificant agents. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. These characteristics can be high-dimensional and need not be included in compact spaces. Stable matchings exist with and without transfers and stable matchings correspond exactly to limits of stable matchings for finite agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite agent matching models, stable matchings exist under a general class of externalities. This might pave the way for integrating matching problems in other economic models.