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. Klaus (Games Econ Behav 72:172-186, 2011) introduced two new "population sensitivity" properties that capture the effect newcomers have on incumbent agents: competition sensitivity and resource sensitivity. On various roommate market domains (marriage markets, no-odd-rings roommate markets, solvable roommate markets), we characterize the core using either of the population sensitivity properties in addition to weak unanimity and consistency. On the domain of all roommate markets, we obtain two associated impossibility results.
Can, B., & Klaus, B. E. (2013). Consistency and population sensitivity properties in marriage and roommate markets. Social Choice and Welfare, 41(4), 835-862. https://doi.org/10.1007/s00355-012-0708-9