Stability in the Roommate Problem: Revisiting the Kalai-Smorodinsky Solution
The classical roommate problem highlights the challenges of forming stable coalitions
when agents pair up based on their preferences. Similarly, in negotiation problems, the
Kalai-Smorodinsky bargaining solution is a widely studied rule, but its application can
fail to ensure stability in certain contexts. This paper explores a framework where agents,
each endowed with a utility function, must form coalitions of two (roommates) and share a
preassigned endowment. We address the question: What rules of division ensure stability
in such settings? Our findings demonstrate that the Kalai-Smorodinsky solution, while
unstable in general bargaining contexts, generates stability in the roommate problem due
to the absence of preference cycles.
Palabras clave: stability roommate problem Kalai-Smorodinsky bargaining solution