Respecting Improvement in Markets with Indivisible Goods

A generalized matching problem consists of a set of agents, a set of objects, the agents’ endowments, a set of feasible matchings, and the agents’ preferences over feasible matchings. Respect for improvement means that when the ranking of an agent’s endowment improves in some other agent’s preference (while keeping other preferences unchanged), then this agent weakly benefits from it. Our main result shows across matching applications that on the strict domain, individual rationality, strategy-proofness, and nonbossiness imply respecting improvement. As a consequence for housing markets, we obtain that top trading with fixed tiebreaking and top trading with random tiebreaking satisfy respecting improvement on the weak domain. We further show that several application-based extensions of the top-trading-cycles mechanism (such as for kidney exchange and school choice) satisfy (a weak version of) respecting improvement.

This paper was accepted by Martin Bichler, market design, platform, and demand analytics.

Funding: The author acknowledges financial support from the Social Sciences and Humanities Research Council of Canada under Insight Grant 435-2023-0129 and the Fonds de recherche du Québec under Soutien aux équipes de recherche / Universitaire- nouvelle équipe 367853.