The core of Shapley-Scarf markets with full preferences

TL;DR

This paper analyzes core concepts in Shapley-Scarf markets with full preferences, introducing new core notions that are always nonempty and Pareto efficient, and compares their relationships.

Contribution

It introduces two new core concepts based on the exclusion and strong cores, ensuring nonemptiness and Pareto efficiency, and compares them with existing cores.

Findings

Exclusion core can be empty but is often nonempty.

New core concepts are nonempty and Pareto efficient.

Core concepts are ordered by set inclusion.

Abstract

We examine core concepts in the classical model of Shapley and Scarf (1974) under full preferences. Among the standard concepts, the strong core may be empty, whereas the nonempty weak core may be overly large and contain inefficient elements. Our main findings are: (1) The exclusion core of Balbuzanov and Kotowski (2019) -- a recent concept outperforming standard concepts in complex environments under strict preferences -- can also be empty, yet it is more often nonempty than the strong core. (2) We introduce two new core concepts, respectively built on the exclusion core and the strong core. Both are nonempty and Pareto efficient, and coincide with the strong core whenever it is nonempty. (3) These core concepts are ordered by set inclusion, with the strong core as the smallest and the weak core as the largest.