What Happens when Agents Join Many-to-One Matching Market?
In their seminal book about matching theory, Roth and Sotomayor (1990) discuss (among other things) what happens in a one-to-one matching market when a new woman joins it. An elegant result shows that in this scenario there exists a non-empty set of men (related to a set of women) each of whom is strictly better off (worse off) under any stable matching in the new market, compared to any stable matching in the old market. This paper explores several extension to this theorem. The main results are that this theorem generalizes for the case of many-to-one matching when a hospital joins the market, but not when a doctor joins it. Furthermore, in the case of generalized matching with contracts a weaker form of the theorem is demonstrated.