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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 (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).

Suggested Citation

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

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    1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
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    3. Pinaki Mandal, 2025. "Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency," Papers 2506.15169, arXiv.org.
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