We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely 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.

In an experiment, we first elicit the distributional preferences of subjects and then let them bid for a lottery, either in a Becker-DeGroot-Marschak (BDM) mechanism or a Vickrey auction (VA). The standard theory predicts that altruistic subjects underbid in the VA-compared to the BDM-while spiteful subjects overbid in the VA. The data do not confirm those predictions. While we observe aggregate underbidding in the VA, the result is not driven by the choices of altruistic subjects.

This paper studies the one-to-one two-sided marriage model (Gale and Shapley, 1962). If agents' preferences exhibit mutually best (i.e., each agent is most preferred by her/his most preferred matching partner), there is a unique stable matching without rank gaps (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are "close" to mutually best. Without a restriction on preference profiles, we find that natural "distances" to mutually best neither bound the size of the core nor the rank gaps at stable matchings. However, for matching markets that satisfy horizontal heterogeneity, "local" distances to mutually best provide bounds for the size of the core and the rank gaps at stable matchings.

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