Competition and resource sensitivity in marriage and roommate markets

We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect newcomers have on incumbent agents. Competition sensitivity focuses on newcomers as additional consumers and requires that some incumbents will suffer if competition is caused by newcomers. Resource sensitivity focuses on newcomers as additional resources and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the domain of all roommate markets, we obtain two associated impossibility results.