2 research outputs found
Morphing Between Stable Matching Problems
In the stable roommates (SR) problem we have n agents,
where each agent ranks all other agents in strict order of preference. The
problem is then to match agents into pairs such that no two agents prefer
each other to their matched partners, and this is a stable matching. The
stable marriage (SM) problem is a special case of SR, where we have
two equal sized sets of agents, men and women, where men rank only
women and women rank only men. Every instance of SM admits at least
one stable matching, whereas for SR as the number of agents increases
the number of instances with stable matchings decreases. So, what will
happen if in SM we allow men to rank men and women to rank women,
i.e. we relax gender separation? Will stability abruptly disappear? And
what happens in a stable roommates scenario if agents do not rank all
other agents? Again, is stability uncommon? And finally, what happens
if there are an odd number of agents? We present empirical evidence to
answer these questions