Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Consistency and population sensitivity properties in marriage and roommate markets

  • 303 Accesses

  • 7 Citations


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.

This is a preview of subscription content, log in to check access.


  1. Chung KS (2000) On the existence of stable roommate matchings. Games Econ Behav 33: 206–230

  2. Crawford VP (1991) Comparative statics in matching markets. J Econ Theory 54: 389–400

  3. Demange, G, Wooders, M (eds) (2004) Group formation in economics; networks, clubs and coalitions. Cambridge University Press, Cambridge

  4. Diamantoudi E, Miyagawa E, Xue L (2004) Random paths to stability in the roommate problem. Games Econ Behav 48: 18–28

  5. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69: 9–15

  6. Jackson MO (2008) Social and economic networks. Princeton University Press, Princeton

  7. Klaus B (2008) Competition and resource sensitivity in marriage and roommate markets. Harvard Business School Working Paper 09-072. http://ideas.repec.org/p/hbs/wpaper/09-072.html

  8. Klaus B (2011) Competition and resource sensitivity in marriage and roommate markets. Games Econ Behav 72: 172–186

  9. Klaus B, Klijn F (2010) Smith and Rawls share a room: stability and medians. Soc Choice Welf 35: 647–667

  10. Özkal-Sanver I (2010) Impossibilities in roommates problems. Math Soc Sci 59: 360–363

  11. Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, Cambridge

  12. Roth AE, Van de Vate JH (1990) Random paths to stability in two-sided matching. Econometrica 58: 1475–1480

  13. Sasaki H, Toda M (1992) Consistency and characterization of the core of two-sided matching problems. J Econ Theory 56: 218–227

  14. Thomson W (2009) Consistent allocation rules. Monograph. Forthcoming

  15. Toda M (2006) Monotonicity and consistency in matching markets. Int J Game Theory 34: 13–31

Download references

Author information

Correspondence to Bettina Klaus.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Can, B., Klaus, B. Consistency and population sensitivity properties in marriage and roommate markets. Soc Choice Welf 41, 835–862 (2013). https://doi.org/10.1007/s00355-012-0708-9

Download citation


  • Pareto Optimality
  • Marriage Market
  • Stable Matchings
  • Good Agent
  • Complete Match