Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation

TL;DR

This paper demonstrates that in object allocation problems, ex-post pairwise efficiency and Pareto efficiency are equivalent under certain conditions, strengthening existing rule characterizations.

Contribution

It establishes the equivalence of pairwise and Pareto efficiency in probabilistic object allocation rules satisfying specific monotonicity and non-wastefulness conditions.

Findings

Ex-post pairwise efficiency equals ex-post Pareto efficiency under given conditions.

Strengthens characterizations of lottery and deterministic rules like Random Serial Dictatorship.

Applicable to various rules including Trading Cycles and Hierarchical Exchange.

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).