Strategy-Proofness and the Core in House Allocation Problems

We study house allocation problems introduced by Shapley and Scarf (1974). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and non-bossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.