The core in the housing market model with fractional endowments

TL;DR

This paper investigates the core concept in a generalized housing market model with fractional endowments, revealing that the strong core can be empty while the weak core remains nonempty, under new blocking definitions.

Contribution

It introduces a new blocking concept for fractional endowments and analyzes core existence, highlighting differences from the classical model.

Findings

Strong core may be empty in the fractional model.

Weak core always exists and contains equal-treatment allocations.

Equal-endowment no envy may not always be satisfied.

Abstract

We explore the core concept in a generalization of the housing market model where agents own fractional endowments while maintaining ordinal preferences. Recognizing that individuals are easier than coalitions to block an allocation, we adopt a definition in which individuals block an allocation if their received assignments do not first-order stochastically dominate their endowment, while a non-singleton coalition blocks an allocation if they can reallocate their endowments to obtain new assignments that first-order stochastically dominate their original assignments. Our findings show that, unlike the original model, the strong core may be empty, while the weak core is nonempty. The weak core always contains elements that satisfy equal treatment of equals, but it may not contain elements satisfying equal-endowment no envy.