Consistent solutions to the allocation of indivisible objects with general endowments

TL;DR

This paper introduces a refined core concept for allocating indivisible objects with general endowments, ensuring nonemptiness and consistency, and providing sharper predictions than existing models.

Contribution

It proposes a new core concept that combines nonemptiness and consistency, improving upon the exclusion core and unifying various market design models.

Findings

The strong core is consistent but can be empty.

The exclusion core is nonempty but not consistent.

The proposed refined core is both nonempty and consistent.

Abstract

We apply the consistency principle to examine various core concepts in a general allocation model that subsumes several familiar market design models as special cases. The conventional strong core is consistent but may be empty, whereas the exclusion core proposed by Balbuzanov and Kotowski (2019), although nonempty, is not consistent and may include unintuitive allocations. We therefore propose a refinement of the exclusion core, which is both nonempty and consistent. Our solution offers sharper predictions than alternatives and coincides with the strong core and/or the exclusion core in special cases that generalize familiar models.