We provide a short proof for the following characterization of the core in housing markets first proved by Ma (1994): the core is the only rule that satisfies strategy-proofness, Pareto efficiency and individual rationality.

We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and non-dictatorship arises in contrast with the Sprumont...