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Abstract

In the stable roommates problem, there are k rooms of varying sizes and n agents, who need to be allocated places in these rooms; it is sometimes assumed that the total number of places is exactly n. Agents may have preferences over rooms as well as potential rommates and may move between rooms so as to improve their assignment. The goal of the project is to understand the complexity of finding stable outcomes in such settings, assuming that agents' preferences over assignments have a simple structure (e.g., each agent wants to maximize the number of friends in their room), and to compare the best social welfare that can be achieved by a centralizes assignment and that achievable in a stable assignment.