Stability in the Roommate Problem: Revisiting the Kalai-Smorodinsky Solution

E. Molis, O. Gallo

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.

Keywords: stability roommate problem Kalai-Smorodinsky bargaining solution

G. Bergantiños, A. Navarro Ramos

M. Domènech Blàzquez, J. M. Giménez Pradales, M. A. Puente del Campo

B. Moreno, L. C. Corchón, G. Correa