Stable Outcomes in Discrete and Continuous Models of Two-Sided Matching: a Unified Treatment

Abstract

We present a unified treatment of a class of two-sided matching models that includes discrete models (such as the marriage model of Gale and Shapley) and continuous models (such as the assignmnent model of Shapley aud Shubik and the generalized assignment model of Demange aud Gale). In contrast with previous, treatments, the parallel conclusions for the two sets of models are derived here in the same way from the same assumptions. We show that the results ill question all follow closely from the assumptions that the core coincides with the core defined by weak domination. In the marriage model, the assumption of strict preferences causes these two sets to coincide, while in the continuous models the two sets coincide because agents have continuous preferences and prices can be adjusted continuously.