The Temporary Exchange Problem

TL;DR

This paper introduces a generalized model for resource exchange where agents care about recipients, not just resources, especially relevant for temporary exchanges, and explores conditions for positive outcomes in this setting.

Contribution

It formalizes a broader allocation model under ordinal preferences, extending beyond the Shapley-Scarf market, and identifies conditions under which positive axiomatic and computational results hold.

Findings

Certain positive results from housing markets do not extend to the new model.

Restrictions on preferences enable positive axiomatic and computational outcomes.

Provides algorithms for individually rational and Pareto optimal allocations.

Abstract

We formalize an allocation model under ordinal preferences that is more general than the well-studied Shapley-Scarf housing market. In our model, the agents do not just care which house or resource they get but also care about who gets their own resource. This assumption is especially important when considering temporary exchanges in which each resource is eventually returned to the owner. We show that several positive axiomatic and computational results that hold for housing markets do not extend to the more general setting. We then identify natural restrictions on the preferences of agents for which several positive results do hold. One of our central results is a general class of algorithms that return any allocation that is individually rational and Pareto optimal with respect to the responsive set extension.