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

2025/08/07 by Tom Demeulemeester, Demeulemeester, Tom, Bettina Klaus +1 · 1 voice
Computer Science · Economics, Econometrics and Finance · #econ.TH #cs.GT

paper · pdf · doi:10.48550/arxiv.2508.05340

Abstract

We consider object allocation problems with capacities where objects have to be assigned to agents. We show that a probabilistically monotonic lottery rule satisfies ex-post Pareto efficiency if and only if it satisfies ex-post pairwise efficiency and ex-post nonwastefulness. This result allows us to strengthen various existing characterization results, both for lottery rules and for deterministic rules, by replacing (ex-post) Pareto efficiency with (ex-post) pairwise efficiency and (ex-post) non-wastefulness, 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).

Citations

• An Axiomatization of the Random Priority Rule
• Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
• Fairness and group-strategyproofness clash in assignment problems

Discussions

• Everyone is assigned one object, and you know that no pair of agents wants to swap their objects. When can you be sure that there will also not exist a group of any size (larger than two) who want to [bsky, 5 points, 0 comments]

Related

• Unambiguous Efficiency of Random Allocations
• Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
• A characterization of strategy-proof probabilistic assignment rules
• Incompatibility of Efficiency and Strategyproofness in the Random Assignment Setting with Indifferences
• An Axiomatization of the Random Priority Rule