Revealed Preferences of One-Sided Matching

TL;DR

This paper develops a framework to test whether observed allocations in one-sided matching can be rationalized by underlying preferences, extending revealed preference theory to both non-transferrable and transferrable utility settings.

Contribution

It introduces a testable model for the revealed preferences of one-sided matching allocations, linking core allocations to preference profiles in both utility settings.

Findings

In non-transferrable utility, allocations are rationalizable if agents with same preferences in cycles receive same allocations.

In transferrable utility, rationalizability is characterized by the existence of supporting price vectors or cyclic monotonicity.

The approach connects classic revealed preference theory with core allocations in matching markets.

Abstract

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.