Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation
Theoretical Economics
2025-08-08 v1 Computer Science and Game Theory
Abstract
We consider object allocation problems with capacities (see, e.g., Abdulkadiroglu and Sonmez, 1998; Basteck, 2025) where objects have to be assigned to agents. We show that if a lottery rule satisfies ex-post non-wastefulness and probabilistic (Maskin) monotonicity, then ex-post pairwise efficiency is equivalent to ex-post Pareto efficiency. This result allows for a strengthening of various existing characterization results, both for lottery rules and deterministic rules, by replacing (ex-post) Pareto efficiency with (ex-post) pairwise efficiency, e.g., for characterizations of the Random Serial Dictatorship rule (Basteck, 2025), Trading Cycles rules (Pycia and Unver, 2017), and Hierarchical Exchange rules (Papai, 2000).
Cite
@article{arxiv.2508.05340,
title = {Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation},
author = {Tom Demeulemeester and Bettina Klaus},
journal= {arXiv preprint arXiv:2508.05340},
year = {2025}
}
Comments
27 pages, 5 figures