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

2025-08-07

AI Summary

This paper studies stochastic object allocation with capacity constraints, focusing on the equivalence of ex-post efficiency notions under lottery-based rules. Methodologically, it integrates mechanism design, Maskin monotonicity analysis, and stochastic dominance comparisons. The main contribution is the first rigorous proof that, under the axioms of ex-post non-wastefulness and probabilistic monotonicity, ex-post pairwise efficiency is equivalent to ex-post Pareto efficiency. This result unifies and strengthens the axiomatic characterizations of classical mechanisms—including Random Serial Dictatorship, Trading Cycles, and Hierarchical Exchange—by establishing a common foundational efficiency benchmark. Moreover, it provides a more concise and expressive theoretical foundation for analyzing the fairness–efficiency trade-off in stochastic allocation, enhancing both conceptual clarity and analytical tractability in the design and evaluation of randomized matching mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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).

Problem

• Analyzes equivalence between pairwise and Pareto efficiency in allocation
• Strengthens existing rules by replacing Pareto with pairwise efficiency
• Applies to lottery and deterministic object allocation mechanisms

Innovation

• Ex-post non-wastefulness ensures efficient allocation
• Probabilistic monotonicity strengthens Pareto efficiency
• Pairwise efficiency replaces Pareto in characterizations