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

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  • Tom Demeulemeester
  • Bettina Klaus

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).

Suggested Citation

  • Tom Demeulemeester & Bettina Klaus, 2025. "Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation," Papers 2508.05340, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2508.05340
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    References listed on IDEAS

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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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