Yuji Fujinaka, Takuma Wakayama
This paper studies housing markets in the presence of constraints on the number of agents involved in exchanges. We search for mechanisms satisfying effective endowments-swapping-proofness, which requires that no pair of agents can gain by “individually rational” swapping their endowments before the mechanism is applied. Our first main result is that when preferences are strict and feasibility constraints are imposed, no mechanism satisfies both individual rationality and effective endowments-swapping-proofness. To avoid this negative result, we consider two well-known restricted domains: common ranking preferences and single-dipped preferences. When each agent has common ranking preferences, there exists a pairwise exchange mechanism that satisfies individual rationality and effective endowments-swapping-proofness in the three-agent case; however, in the case with four or more agents, we again obtain a negative result. We further establish that the top trading cycles mechanism is the only pairwise exchange mechanism satisfying individual rationality and effective endowments-swapping-proofness when preferences are single-dipped.