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On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness

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  • Moshe Babaioff
  • Noam Manaker Morag

Abstract

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.

Suggested Citation

  • Moshe Babaioff & Noam Manaker Morag, 2024. "On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness," Papers 2411.11131, arXiv.org.
  • Handle: RePEc:arx:papers:2411.11131
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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.
    2. Moshe Babaioff & Uriel Feige, 2024. "Share-Based Fairness for Arbitrary Entitlements," Papers 2405.14575, arXiv.org.
    3. repec:bla:jpbect:v:3:y:2001:i:3:p:257-71 is not listed on IDEAS
    4. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    5. Szilvia PÂpai, 2000. "original papers : Strategyproof multiple assignment using quotas," Review of Economic Design, Springer;Society for Economic Design, vol. 5(1), pages 91-105.
    6. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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