Stable Assignment of Public Facilities under Congestion

We study the problem of locating multiple public facilities when each member of society has to be assigned to exactly one of these facilities. Individuals' preferences are assumed to be single-peaked over the interval of possible locations and negatively affected by congestion. We characterize strategy-proof, efficient, and stable allocation rules when agents have to be partitioned between two groups of users and discuss the normative content of the stability property. Finally we prove that when more than two groups have to be formed, even with common information on the distribution of the peaks, there is no strategy-proof, efficient, and stable allocation rule.