Matching Markets with N-Dimensional Preferences

Abstract. This paper analyzes matching markets where agent types are n-vectors of characteristics--i.e. points in R^n --and agents prefer matches that are closer to them according to a distance metric on this set (horizontal preferences). First, given a few assumptions, I show that in the Gale-Shapley stable matching in this environment, agents match to a linear function of their own type. I show that restrictions on preferences are not as onerous as they may seem, as a rich variety of preference structures can be mapped into the horizontal framework. With these results in hand, I develop a highly stylized model of an online dating platform that helps consumers find and contact potential matches, where consumers have preferences over many characteristics (e.g. height, income, age, etc.) and have the option to pay to join the platform or look for a match off the platform. I characterize the firm's optimal pricing strategy and the concomitant market outcomes for consumers. Finally, I address an unanswered question in the matching literature--can multidimensional preferences be aggregated (e.g. into a univariate measure of quality) without changing the salient features of the model? I find that, in the dating platform model I introduced, consumer preferences can be aggregated without any change to firm strategy or market outcomes, providing some justification for the univariate-type matching models prevalent in the theoretical matching literature.