An analysis of a real-life allocation problem

We consider a real-life problemfaced by the Sabanc¬ University Dormitory O¢ce (SUDO). Every year SUDO (i) allocates the dormitory beds among applicants and then (ii) determines the roommates that will share each room. For the allocation part, we examine the allocation rule that is currently used and we show that it does not satisfy Pareto e¢ciency, strategy- proofness and justified no envy. To eliminate these shortcomings, we introduce a modified version of the well-known serial dictatorship rule. We then analyze the roommate assignment rule that is currently used by SUDO. We determine that this rule also has serious shortcomings such as producing unstable and Pareto inefficient matchings. We then modify the rule to eliminate these failures. Moreover, we introduce a new kind of roommate problem in which each agent has three roommates. We then obtain some conditions which guarantee the existence of a stable matching for this kind of roommate problem