  Consider the object allocation (one-sided matching) model of Shapley and
Scarf (1974). When final allocations are observed but agents' preferences are
unknown, when might the allocation be in the core? This is a one-sided analogue
of the model in Echenique, Lee, Shum, and Yenmez (2013). I build a model in
which the strict core is testable -- an allocation is "rationalizable" if there
is a preference profile putting it in the core. In this manner, I develop a
theory of the revealed preferences of one-sided matching. I study
rationalizability in both non-transferrable and transferrable utility settings.
In the non-transferrable utility setting, an allocation is rationalizable if
and only if: whenever agents with the same preferences are in the same
potential trading cycle, they receive the same allocation. In the transferrable
utility setting, an allocation is rationalizable if and only if: there exists a
price vector supporting the allocation as a competitive equilibrium; or
equivalently, it satisfies a cyclic monotonicity condition. The proofs leverage
simple graph theory and combinatorial optimization and tie together classic
theories of consumer demand revealed preferences and competitive equilibrium.
