On the existence of stable roommate matchings

This paper identifies a condition called "no odd rings" that is sufficient for the existence of stable roommate matchings in the weak preferences case . It shows that the process of allowing randomly chosen blocking pairs to m atch converges to a stable roommate matching with probability one as long a s there are no odd ring. This random-paths-to-stability result generalizes that of Roth and Vande Vate (1990, Econometrica 58, 1475-1480) and may not hold if there are odd rings. The "no odd rings" condition can also be used to prove a number of other sufficient conditions that are more economically interpretable. Journal of Economic Literature Classification Numbers: C78, D71. (C) 2000 Academic Press.