Notes and Comments Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems

WHEN A COLLEGE GRADUATE decides to pursue a higher degree at a particular institution, one of the first challenges she faces is finding an apartment. Most institutions have on-campus housing available that is often subsidized and hence more appealing than its alternatives. Usually there are several types of on-campus housing and the attractiveness of each type changes from person to person. Therefore housing offices need to find 44mechanisms" to allocate available housing among the applicants who might have various preferences. In this paper we deal with this class of problems to which we refer as house allocation problems.2 Formally, there are n agents who collectively own n indivisible objects, say houses, and each agent has preferences over objects.3 An allocation is a matching of houses to agents and a matching mechanism is a systematic procedure to select a matching for each problem. A widely studied class of matching mechanisms is the class of simple serial dictatorships: For a given ordering of agents, the agent who is ordered first is assigned her top choice, the agent ordered second is assigned her top choice among the remaining houses, and so on. These matching mechanisms are not considered very desirable as they discriminate between the agents. However this difficulty can be handled by randomly determining an ordering and using the induced simple serial dictatorship. We refer to this mechanism as the random serial dictato;-ship. Of course this mechanism selects lotteries over matchings instead of matchings and we refer to such mechanisms as lottery mechanisms. Our first contribution is the introduction of a (seemingly) alternative lottery mechanism. For this purpose we need to introduce a related class of problems, namely the